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Number Theory And Analysis
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Book Synopsis A Course in Analytic Number Theory by : Marius Overholt
Download or read book A Course in Analytic Number Theory written by Marius Overholt and published by American Mathematical Soc.. This book was released on 2014-12-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Book Synopsis Introduction to Analytic Number Theory by : Tom M. Apostol
Download or read book Introduction to Analytic Number Theory written by Tom M. Apostol and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS
Book Synopsis Analytic Number Theory by : P. T. Bateman
Download or read book Analytic Number Theory written by P. T. Bateman and published by World Scientific. This book was released on 2004 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (?elementary?) and complex variable (?analytic?) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/
Book Synopsis Applications of Number Theory to Numerical Analysis by : L.-K. Hua
Download or read book Applications of Number Theory to Numerical Analysis written by L.-K. Hua and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions.
Book Synopsis Number Theory, Analysis and Geometry by : Dorian Goldfeld
Download or read book Number Theory, Analysis and Geometry written by Dorian Goldfeld and published by Springer Science & Business Media. This book was released on 2011-12-21 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang’s vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas of the field, namely Number Theory, Analysis, and Geometry, representing Lang’s own breadth of interest and impact. A special introduction by John Tate includes a brief and fascinating account of the Serge Lang’s life. This volume's group of 6 editors are also highly prominent mathematicians and were close to Serge Lang, both academically and personally. The volume is suitable to research mathematicians in the areas of Number Theory, Analysis, and Geometry.
Book Synopsis Computational Excursions in Analysis and Number Theory by : Peter Borwein
Download or read book Computational Excursions in Analysis and Number Theory written by Peter Borwein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
Book Synopsis Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis by : Hugh L. Montgomery
Download or read book Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis written by Hugh L. Montgomery and published by American Mathematical Soc.. This book was released on 1994 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.
Book Synopsis Analytic Number Theory by : Henryk Iwaniec
Download or read book Analytic Number Theory written by Henryk Iwaniec and published by American Mathematical Soc.. This book was released on 2021-10-14 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Book Synopsis A Primer of Analytic Number Theory by : Jeffrey Stopple
Download or read book A Primer of Analytic Number Theory written by Jeffrey Stopple and published by Cambridge University Press. This book was released on 2003-06-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.
Book Synopsis Steps into Analytic Number Theory by : Paul Pollack
Download or read book Steps into Analytic Number Theory written by Paul Pollack and published by Springer Nature. This book was released on 2021-02-08 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem book gathers together 15 problem sets on analytic number theory that can be profitably approached by anyone from advanced high school students to those pursuing graduate studies. It emerged from a 5-week course taught by the first author as part of the 2019 Ross/Asia Mathematics Program held from July 7 to August 9 in Zhenjiang, China. While it is recommended that the reader has a solid background in mathematical problem solving (as from training for mathematical contests), no possession of advanced subject-matter knowledge is assumed. Most of the solutions require nothing more than elementary number theory and a good grasp of calculus. Problems touch at key topics like the value-distribution of arithmetic functions, the distribution of prime numbers, the distribution of squares and nonsquares modulo a prime number, Dirichlet's theorem on primes in arithmetic progressions, and more. This book is suitable for any student with a special interest in developing problem-solving skills in analytic number theory. It will be an invaluable aid to lecturers and students as a supplementary text for introductory Analytic Number Theory courses at both the undergraduate and graduate level.
Book Synopsis Complex Analysis with Applications to Number Theory by : Tarlok Nath Shorey
Download or read book Complex Analysis with Applications to Number Theory written by Tarlok Nath Shorey and published by Springer Nature. This book was released on 2020-11-13 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses major topics in complex analysis with applications to number theory. This book is intended as a text for graduate students of mathematics and undergraduate students of engineering, as well as to researchers in complex analysis and number theory. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two and three manifolds and number theory. In additional to solved examples and problems, the book covers most of the topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, gamma function and harmonic functions.
Book Synopsis Complex Analysis in Number Theory by : Anatoly A. Karatsuba
Download or read book Complex Analysis in Number Theory written by Anatoly A. Karatsuba and published by CRC Press. This book was released on 1994-11-22 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.
Book Synopsis Abstract analytic number theory by : Knopfmacher
Download or read book Abstract analytic number theory written by Knopfmacher and published by Newnes. This book was released on 2009-02-04 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and "statistical" properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
Book Synopsis Analytic Number Theory by : Jean-Marie De Koninck
Download or read book Analytic Number Theory written by Jean-Marie De Koninck and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy-Ramanujan and Landau theorems, characters and the Dirichlet theorem, the $abc$ conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer. One of this book's best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book.
Book Synopsis Introduction to Analytic and Probabilistic Number Theory by : G. Tenenbaum
Download or read book Introduction to Analytic and Probabilistic Number Theory written by G. Tenenbaum and published by Cambridge University Press. This book was released on 1995-06-30 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.
Book Synopsis The Prime Number Theorem by : G. J. O. Jameson
Download or read book The Prime Number Theorem written by G. J. O. Jameson and published by Cambridge University Press. This book was released on 2003-04-17 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Book Synopsis Excursions in Number Theory by : Charles Stanley Ogilvy
Download or read book Excursions in Number Theory written by Charles Stanley Ogilvy and published by Courier Corporation. This book was released on 1988-01-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
