# analytic number theory for undergraduates 3 monographs in number theory

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## Analytic Number Theory For Undergraduates

**Author :**Heng Huat Chan

**ISBN :**9789814365277

**Genre :**Mathematics

**File Size :**20. 67 MB

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This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression. The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

## Analytic Number Theory

**Author :**P. T. Bateman

**ISBN :**9812560807

**Genre :**Mathematics

**File Size :**22. 27 MB

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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/

## A Primer Of Analytic Number Theory

**Author :**Jeffrey Stopple

**ISBN :**0521012538

**Genre :**Mathematics

**File Size :**32. 66 MB

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This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.

## Analytic Number Theory

**Author :**Jean-Marie De Koninck

**ISBN :**9780821875773

**Genre :**Mathematics

**File Size :**32. 7 MB

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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.

## Not Always Buried Deep

**Author :**Paul Pollack

**ISBN :**9780821848807

**Genre :**Mathematics

**File Size :**85. 34 MB

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Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.

## A Course In Analytic Number Theory

**Author :**Marius Overholt

**ISBN :**9781470417062

**Genre :**Mathematics

**File Size :**64. 42 MB

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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.

## Number Theory Fermat S Dream

**Author :**Kazuya Kato

**ISBN :**082180863X

**Genre :**Mathematics

**File Size :**32. 64 MB

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This is the English translation of the original Japanese book. In this volume, ``Fermat's Dream'', core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.

## Introduction To Analytic Number Theory

**Author :**Tom M. Apostol

**ISBN :**9781475755794

**Genre :**Mathematics

**File Size :**46. 80 MB

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"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

## Basic Analytic Number Theory

**Author :**Anatolij A. Karatsuba

**ISBN :**9783642580185

**Genre :**Mathematics

**File Size :**22. 89 MB

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This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. August, 1991 Melvyn B. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans lation of my book. In the Soviet Union, the primary purpose of this monograph was to introduce mathematicians to the basic results and methods of analytic number theory, but the book has also been increasingly used as a textbook by graduate students in many different fields of mathematics. I hope that the English edition will be used in the same ways. I express my deep gratitude to Professor Melvyn B. Nathanson for his excellent translation and for much assistance in correcting errors in the original text. A.A. Karatsuba Introduction to the Second Russian Edition Number theory is the study of the properties of the integers. Analytic number theory is that part of number theory in which, besides purely number theoretic arguments, the methods of mathematical analysis play an essential role.

## Unsolved Problems In Number Theory

**Author :**Richard Guy

**ISBN :**9780387266770

**Genre :**Mathematics

**File Size :**21. 74 MB

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Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.