Prime Detecting Sieves Lms 33

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Prime-Detecting Sieves (LMS-33)

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Author : Glyn Harman
Publisher : Princeton University Press
ISBN 13 : 0691202990
Total Pages : 378 pages
Book Rating : 4.6/5 (912 download)

Book Synopsis Prime-Detecting Sieves (LMS-33) by : Glyn Harman

Download or read book Prime-Detecting Sieves (LMS-33) written by Glyn Harman and published by Princeton University Press. This book was released on 2020-05-26 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube. This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.

Log-Gases and Random Matrices (LMS-34)

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Author : Peter J. Forrester
Publisher : Princeton University Press
ISBN 13 : 1400835410
Total Pages : 808 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Log-Gases and Random Matrices (LMS-34) by : Peter J. Forrester

Download or read book Log-Gases and Random Matrices (LMS-34) written by Peter J. Forrester and published by Princeton University Press. This book was released on 2010-07-01 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.

Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas

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Author : Daniel Kriz
Publisher : Princeton University Press
ISBN 13 : 0691216479
Total Pages : 280 pages
Book Rating : 4.6/5 (912 download)

Book Synopsis Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas by : Daniel Kriz

Download or read book Supersingular P-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas written by Daniel Kriz and published by Princeton University Press. This book was released on 2021-11-09 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.

Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35)

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Author : Zhen-Qing Chen
Publisher : Princeton University Press
ISBN 13 : 069113605X
Total Pages : 496 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) by : Zhen-Qing Chen

Download or read book Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35) written by Zhen-Qing Chen and published by Princeton University Press. This book was released on 2012 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

Lectures on P-adic L-functions

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Author : Kenkichi Iwasawa
Publisher : Princeton University Press
ISBN 13 : 9780691081120
Total Pages : 120 pages
Book Rating : 4.0/5 (811 download)

Book Synopsis Lectures on P-adic L-functions by : Kenkichi Iwasawa

Download or read book Lectures on P-adic L-functions written by Kenkichi Iwasawa and published by Princeton University Press. This book was released on 1972-07-21 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.

Millions, Billions, Zillions

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Author : Brian Kernighan
Publisher : Princeton University Press
ISBN 13 : 069120909X
Total Pages : 176 pages
Book Rating : 4.6/5 (912 download)

Book Synopsis Millions, Billions, Zillions by : Brian Kernighan

Download or read book Millions, Billions, Zillions written by Brian Kernighan and published by Princeton University Press. This book was released on 2020-11-10 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Numbers are often intimidating, confusing, and even deliberately deceptive--especially when they are really big. The media loves to report on millions, billions, and trillions, but frequently makes basic mistakes or presents such numbers in misleading ways. And misunderstanding numbers can have serious consequences, since they can deceive us in many of our most important decisions, including how to vote, what to buy, and whether to make a financial investment. In this short, accessible, enlightening, and entertaining book, leading computer scientist Brian Kernighan teaches anyone--even diehard math-phobes--how to demystify the numbers that assault us every day. With examples drawn from a rich variety of sources, including journalism, advertising, and politics, Kernighan demonstrates how numbers can mislead and misrepresent. In chapters covering big numbers, units, dimensions, and more, he lays bare everything from deceptive graphs to speciously precise numbers. And he shows how anyone--using a few basic ideas and lots of shortcuts--can easily learn to recognize common mistakes, determine whether numbers are credible, and make their own sensible estimates when needed. Giving you the simple tools you need to avoid being fooled by dubious numbers, Millions, Billions, Zillions is an essential survival guide for a world drowning in big--and often bad--data"--Jacket

An Invitation to Modern Number Theory

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Author : Steven J. Miller
Publisher : Princeton University Press
ISBN 13 : 0691215979
Total Pages : pages
Book Rating : 4.6/5 (912 download)

Book Synopsis An Invitation to Modern Number Theory by : Steven J. Miller

Download or read book An Invitation to Modern Number Theory written by Steven J. Miller and published by Princeton University Press. This book was released on 2020-08-04 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Arithmetic and Geometry

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Author : Gisbert Wüstholz
Publisher : Princeton University Press
ISBN 13 : 0691193789
Total Pages : 186 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Arithmetic and Geometry by : Gisbert Wüstholz

Download or read book Arithmetic and Geometry written by Gisbert Wüstholz and published by Princeton University Press. This book was released on 2019-10-08 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Lectures by outstanding scholars on progress made in the past ten years in the most progressive areas of arithmetic and geometry - primarily arithmetic geometry"--

Algebraic Theory of Numbers. (AM-1), Volume 1

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Author : Hermann Weyl
Publisher : Princeton University Press
ISBN 13 : 140088280X
Total Pages : 240 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Algebraic Theory of Numbers. (AM-1), Volume 1 by : Hermann Weyl

Download or read book Algebraic Theory of Numbers. (AM-1), Volume 1 written by Hermann Weyl and published by Princeton University Press. This book was released on 2016-04-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.

Prime Suspects

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Author : Andrew Granville
Publisher : Princeton University Press
ISBN 13 : 0691188734
Total Pages : 233 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Prime Suspects by : Andrew Granville

Download or read book Prime Suspects written by Andrew Granville and published by Princeton University Press. This book was released on 2019-08-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: An outrageous graphic novel that investigates key concepts in mathematics Integers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body. Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Travel with Detective von Neumann as he leaves no clue unturned, from shepherds’ huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the frustration—and the excitement—of our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all. Beautifully drawn and exquisitely detailed, Prime Suspects is unique, astonishing, and witty—a once-in-a-lifetime opportunity to experience mathematics like never before.

Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions

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Author : Günter Harder
Publisher : Princeton University Press
ISBN 13 : 0691197881
Total Pages : 234 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions by : Günter Harder

Download or read book Eisenstein Cohomology for GLN and the Special Values of Rankin–Selberg L-Functions written by Günter Harder and published by Princeton University Press. This book was released on 2019-12-03 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- The cohomology of GLn -- Analytic tools -- Boundary cohomology -- The strongly inner spectrum and applications -- Eisenstein cohomology -- L-functions -- Harish-Chandra modules over Z / by Günter Harder -- Archimedean intertwining operator / by Uwe Weselmann.

Abelian Varieties with Complex Multiplication and Modular Functions

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Author : Goro Shimura
Publisher : Princeton University Press
ISBN 13 : 1400883946
Total Pages : 232 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Abelian Varieties with Complex Multiplication and Modular Functions by : Goro Shimura

Download or read book Abelian Varieties with Complex Multiplication and Modular Functions written by Goro Shimura and published by Princeton University Press. This book was released on 2016-06-02 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900 Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals. The investigation of such algebraicity is relatively new, but has attracted the interest of increasingly many researchers. Many of the topics discussed in this book have not been covered before. In particular, this is the first book in which the topics of various algebraic relations among the periods of abelian integrals, as well as the special values of theta and Siegel modular functions, are treated extensively.

Number Theory

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Author : John J. Watkins
Publisher : Princeton University Press
ISBN 13 : 0691159408
Total Pages : 592 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Number Theory by : John J. Watkins

Download or read book Number Theory written by John J. Watkins and published by Princeton University Press. This book was released on 2013-12-26 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook with a unique historical approach to teaching number theory The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)

Some Problems of Unlikely Intersections in Arithmetic and Geometry

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Author : Umberto Zannier
Publisher : Princeton University Press
ISBN 13 : 1400842719
Total Pages : 175 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Some Problems of Unlikely Intersections in Arithmetic and Geometry by : Umberto Zannier

Download or read book Some Problems of Unlikely Intersections in Arithmetic and Geometry written by Umberto Zannier and published by Princeton University Press. This book was released on 2012-03-25 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila).

Euler Systems

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Author : Karl Rubin
Publisher : Princeton University Press
ISBN 13 : 9780691050768
Total Pages : 244 pages
Book Rating : 4.0/5 (57 download)

Book Synopsis Euler Systems by : Karl Rubin

Download or read book Euler Systems written by Karl Rubin and published by Princeton University Press. This book was released on 2000-05-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.

Summing It Up

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Author : Avner Ash
Publisher : Princeton University Press
ISBN 13 : 0691178518
Total Pages : 248 pages
Book Rating : 4.6/5 (911 download)

Book Synopsis Summing It Up by : Avner Ash

Download or read book Summing It Up written by Avner Ash and published by Princeton University Press. This book was released on 2018-01-30 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The power and properties of numbers, from basic addition and sums of squares to cutting-edge theory We use addition on a daily basis—yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series—long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms—the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.

Transcendental Numbers. (AM-16)

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Author : Carl Ludwig Siegel
Publisher : Princeton University Press
ISBN 13 : 1400882354
Total Pages : 102 pages
Book Rating : 4.4/5 (8 download)

Book Synopsis Transcendental Numbers. (AM-16) by : Carl Ludwig Siegel

Download or read book Transcendental Numbers. (AM-16) written by Carl Ludwig Siegel and published by Princeton University Press. This book was released on 2016-03-02 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Transcendental Numbers. (AM-16), will be forthcoming.