Introduction To Algebraic Independence Theory

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Introduction to Algebraic Independence Theory

Author : Yuri V. Nesterenko
Publisher : Springer
ISBN 13 : 3540445501
Total Pages : 257 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Introduction to Algebraic Independence Theory by : Yuri V. Nesterenko

Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by Springer. This book was released on 2003-07-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.

Introduction to Algebraic Independence Theory

Author : Yuri V. Nesterenko
Publisher :
ISBN 13 : 9783662183724
Total Pages : 276 pages
Book Rating : 4.1/5 (837 download)

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Book Synopsis Introduction to Algebraic Independence Theory by : Yuri V. Nesterenko

Download or read book Introduction to Algebraic Independence Theory written by Yuri V. Nesterenko and published by . This book was released on 2014-01-15 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Independence

Author : I︠U︡riĭ Valentinovich Nesterenko
Publisher :
ISBN 13 : 9788173199844
Total Pages : 0 pages
Book Rating : 4.1/5 (998 download)

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Book Synopsis Algebraic Independence by : I︠U︡riĭ Valentinovich Nesterenko

Download or read book Algebraic Independence written by I︠U︡riĭ Valentinovich Nesterenko and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an expanded version of the notes of a course of lectures given by at the Tata Institute of Fundamental Research in 1998. It deals with several important results and methods in transcendental number theory. First, the classical result of Lindemann-Weierstrass and its applications are dealt with. Subsequently, Siegel's theory of $E$-functions is developed systematically, culminating in Shidlovskii's theorem on the algebraic independence of the values of the $E$-functions satisfying a system of differential equations at certain algebraic values. Proof of the Gelfond-Schneider Theorem is given based on the method of interpolation determinants introduced in 1992 by M. Laurent. The author's famous result in 1996 on the algebraic independence of the values of the Ramanujan functions is the main theme of the reminder of the book. After deriving several beautiful consequences of his result, the author develops the algebraic material necessary for the proof. The two important technical tools in the proof are Philippon's criterion for algebraic independence and zero bound for Ramanujan functions. The proofs of these are covered in detail. The author also presents a direct method, without using any criterion for algebraic independence as that of Philippon, by which one can obtain lower bounds for transcendence degree of finitely generated field $\mathbb Q(\omega_1,\ldots,\omega_m)$. This is a contribution towards Schanuel's conjecture. The book is self-contained and the proofs are clear and lucid. A brief history of the topics is also given. Some sections intersect with Chapters 3 and 10 of Introduction to Algebraic Independence Theory, Lecture Notes in Mathematics, Springer, 1752, edited by Yu. V. Nesterenko and P. Philippon.

An Introduction to Algebraic Number Theory

Author : Takashi Ono
Publisher : Springer Science & Business Media
ISBN 13 : 146130573X
Total Pages : 233 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis An Introduction to Algebraic Number Theory by : Takashi Ono

Download or read book An Introduction to Algebraic Number Theory written by Takashi Ono and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in 1988. The translation is faithful to the original globally but, taking advantage of my being the translator of my own book, I felt completely free to reform or deform the original locally everywhere. When I sent T. Tamagawa a copy of the First Edition of the original work two years ago, he immediately pointed out that I had skipped the discussion of the class numbers of real quadratic fields in terms of continued fractions and (in a letter dated 2/15/87) sketched his idea of treating continued fractions without writing explicitly continued fractions, an approach he had first presented in his number theory lectures at Yale some years ago. Although I did not follow his approach exactly, I added to this translation a section (Section 4. 9), which nevertheless fills the gap pointed out by Tamagawa. With this addition, the present book covers at least T. Takagi's Shoto Seisuron Kogi (Lectures on Elementary Number Theory), First Edition (Kyoritsu, 1931), which, in turn, covered at least Dirichlet's Vorlesungen. It is customary to assume basic concepts of algebra (up to, say, Galois theory) in writing a textbook of algebraic number theory. But I feel a little strange if I assume Galois theory and prove Gauss quadratic reciprocity.

Set Theory An Introduction To Independence Proofs

Author : K. Kunen
Publisher : Elsevier
ISBN 13 : 0080570585
Total Pages : 330 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Set Theory An Introduction To Independence Proofs by : K. Kunen

Download or read book Set Theory An Introduction To Independence Proofs written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

Algebraic Independence of the Values at Algebraic Points of a Class of Functions Considered by Mahler

Author : N. Ch Wass
Publisher :
ISBN 13 :
Total Pages : 72 pages
Book Rating : 4.3/5 (121 download)

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Book Synopsis Algebraic Independence of the Values at Algebraic Points of a Class of Functions Considered by Mahler by : N. Ch Wass

Download or read book Algebraic Independence of the Values at Algebraic Points of a Class of Functions Considered by Mahler written by N. Ch Wass and published by . This book was released on 1990 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1,\... m)(\*)\cr} TABLE/EQUATION ENDS)for b $\geq$ 2, a$\sb{\rm ij}$(z), b$\sb{\rm j}$(z) in K(z). Suppose finally that $\alpha\in\kappa$ is such that 0 $

Contributions to the Theory of Transcendental Numbers

Author : Gregory Chudnovsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821815008
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Contributions to the Theory of Transcendental Numbers by : Gregory Chudnovsky

Download or read book Contributions to the Theory of Transcendental Numbers written by Gregory Chudnovsky and published by American Mathematical Soc.. This book was released on 1984 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a collection of papers devoted primarily to transcendental number theory and diophantine approximations. This title includes a text of the author's invited address on his work on the theory of transcendental numbers to the 1978 International Congress of Mathematicians in Helsinki.

An Introduction to Commutative Algebra

Author : Huishi Li
Publisher : World Scientific
ISBN 13 : 9789812389510
Total Pages : 198 pages
Book Rating : 4.3/5 (895 download)

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Book Synopsis An Introduction to Commutative Algebra by : Huishi Li

Download or read book An Introduction to Commutative Algebra written by Huishi Li and published by World Scientific. This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry

Lectures on the Theory of Algebraic Numbers

Author : E. T. Hecke
Publisher : Springer Science & Business Media
ISBN 13 : 1475740921
Total Pages : 251 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Lectures on the Theory of Algebraic Numbers by : E. T. Hecke

Download or read book Lectures on the Theory of Algebraic Numbers written by E. T. Hecke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: . . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.

Set Theory

Author : Kenneth Kunen
Publisher : Elsevier Science Limited
ISBN 13 : 9780444854018
Total Pages : 313 pages
Book Rating : 4.8/5 (54 download)

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Book Synopsis Set Theory by : Kenneth Kunen

Download or read book Set Theory written by Kenneth Kunen and published by Elsevier Science Limited. This book was released on 1980-01-01 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Transcendental Number Theory

Author : Alan Baker
Publisher : Cambridge University Press
ISBN 13 : 1009229966
Total Pages : pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis Transcendental Number Theory by : Alan Baker

Download or read book Transcendental Number Theory written by Alan Baker and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.

Introduction to Abstract Algebra

Author : Benjamin Fine
Publisher : JHU Press
ISBN 13 : 1421411776
Total Pages : 583 pages
Book Rating : 4.4/5 (214 download)

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Book Synopsis Introduction to Abstract Algebra by : Benjamin Fine

Download or read book Introduction to Abstract Algebra written by Benjamin Fine and published by JHU Press. This book was released on 2014-07-01 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic

Algebraic Theory of Independence in Information Systems

Author : M. Novotny
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (257 download)

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Book Synopsis Algebraic Theory of Independence in Information Systems by : M. Novotny

Download or read book Algebraic Theory of Independence in Information Systems written by M. Novotny and published by . This book was released on 1989 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Algebraic Quantum Field Theory

Author : S.S. Horuzhy
Publisher : Springer Science & Business Media
ISBN 13 : 9789027727220
Total Pages : 326 pages
Book Rating : 4.7/5 (272 download)

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Book Synopsis Introduction to Algebraic Quantum Field Theory by : S.S. Horuzhy

Download or read book Introduction to Algebraic Quantum Field Theory written by S.S. Horuzhy and published by Springer Science & Business Media. This book was released on 1990-06-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ... , si j'avait su comment en revenir, One service mathematics has rendered the human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shel.f next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

An Introduction to Independence for Analysts

Author : H. G. Dales
Publisher : Cambridge University Press
ISBN 13 : 0521339960
Total Pages : 257 pages
Book Rating : 4.5/5 (213 download)

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Book Synopsis An Introduction to Independence for Analysts by : H. G. Dales

Download or read book An Introduction to Independence for Analysts written by H. G. Dales and published by Cambridge University Press. This book was released on 1987-12-10 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

Algebraic Number Theory

Author : H. Koch
Publisher : Springer Science & Business Media
ISBN 13 : 9783540630036
Total Pages : 280 pages
Book Rating : 4.6/5 (3 download)

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Book Synopsis Algebraic Number Theory by : H. Koch

Download or read book Algebraic Number Theory written by H. Koch and published by Springer Science & Business Media. This book was released on 1997-09-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993

Lectures on Algebraic Model Theory

Author : Bradd T. Hart
Publisher : Springer Science & Business
ISBN 13 : 9780821827055
Total Pages : 124 pages
Book Rating : 4.8/5 (27 download)

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Book Synopsis Lectures on Algebraic Model Theory by : Bradd T. Hart

Download or read book Lectures on Algebraic Model Theory written by Bradd T. Hart and published by Springer Science & Business. This book was released on 2002 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thin volume contains three sets of lecture notes, representing recent developments in differential scales, o-minimality, and tame convergence theory. The first lecture outlines the basics of differential fields, and then addresses topics like differential varieties and tangent bundles, Kolchin's logarithmic derivative, and Manin's construction. The second describes added exponentation, T-convexity and tame extensions, piecewise linearity, the Wilkie inequality, and the valuation property. And the third considers the structure and varieties of finite algebra. No index. c. Book News Inc.