Analytic Number Theory

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Analytic Number Theory

Henryk Iwaniec,Emmanuel Kowalski
Analytic Number Theory Book PDF

Author : Henryk Iwaniec,Emmanuel Kowalski
Publisher : American Mathematical Soc.
Page : 615 pages
File Size : 53,6 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470467708

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Analytic Number Theory by Henryk Iwaniec,Emmanuel Kowalski Pdf

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.

Introduction to Analytic Number Theory

A. G. Postnikov
Introduction to Analytic Number Theory Book PDF

Author : A. G. Postnikov
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 55,9 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 9780821813492

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Introduction to Analytic Number Theory by A. G. Postnikov Pdf

Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.

Analytic Number Theory for Undergraduates

Heng Huat Chan
Analytic Number Theory for Undergraduates Book PDF

Author : Heng Huat Chan
Publisher : World Scientific Publishing Company
Page : 128 pages
File Size : 51,8 Mb
Release : 2009-04-21
Category : Mathematics
ISBN : 9789814365277

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Analytic Number Theory for Undergraduates by Heng Huat Chan Pdf

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.

Introduction to Analytic Number Theory

Tom M. Apostol
Introduction to Analytic Number Theory Book PDF

Author : Tom M. Apostol
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 41,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475755794

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Introduction to Analytic Number Theory by Tom M. Apostol Pdf

"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

Introduction to Analytic and Probabilistic Number Theory

G. Tenenbaum
Introduction to Analytic and Probabilistic Number Theory Book PDF

Author : G. Tenenbaum
Publisher : Cambridge University Press
Page : 180 pages
File Size : 43,8 Mb
Release : 1995-06-30
Category : Mathematics
ISBN : 0521412617

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Introduction to Analytic and Probabilistic Number Theory by G. Tenenbaum Pdf

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.

A Course in Analytic Number Theory

Marius Overholt
A Course in Analytic Number Theory Book PDF

Author : Marius Overholt
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 55,9 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062

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A Course in Analytic Number Theory by Marius Overholt Pdf

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.

Introduction to $p$-adic Analytic Number Theory

M. Ram Murty
Introduction to p adic Analytic Number Theory Book PDF

Author : M. Ram Murty
Publisher : American Mathematical Soc.
Page : 149 pages
File Size : 51,6 Mb
Release : 2009-02-09
Category : Number theory
ISBN : 9780821847749

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Introduction to $p$-adic Analytic Number Theory by M. Ram Murty Pdf

This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.

A Primer of Analytic Number Theory

Jeffrey Stopple
A Primer of Analytic Number Theory Book PDF

Author : Jeffrey Stopple
Publisher : Cambridge University Press
Page : 404 pages
File Size : 50,5 Mb
Release : 2003-06-23
Category : Mathematics
ISBN : 0521012538

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A Primer of Analytic Number Theory by Jeffrey Stopple Pdf

An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.

Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis

Hugh L. Montgomery
Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis Book PDF

Author : Hugh L. Montgomery
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 46,5 Mb
Release : 1994
Category : Analyse harmonique - Congrès
ISBN : 9780821807378

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Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis by Hugh L. Montgomery Pdf

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.

Steps into Analytic Number Theory

Paul Pollack,Akash Singha Roy
Steps into Analytic Number Theory Book PDF

Author : Paul Pollack,Akash Singha Roy
Publisher : Springer Nature
Page : 191 pages
File Size : 53,8 Mb
Release : 2021-02-08
Category : Mathematics
ISBN : 9783030650773

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Steps into Analytic Number Theory by Paul Pollack,Akash Singha Roy Pdf

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.

Analytic Number Theory

Donald J. Newman
Analytic Number Theory Book PDF

Author : Donald J. Newman
Publisher : Springer Science & Business Media
Page : 80 pages
File Size : 45,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387227405

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Analytic Number Theory by Donald J. Newman Pdf

Some of the central topics in number theory, presnted in a simple and concise fashion. The author covers an amazing amount of material, despite a leisurely pace and emphasis on readability. His heartfelt enthusiasm enables readers to see what is magical about the subject. All the topics are presented in a refreshingly elegant and efficient manner with clever examples and interesting problems throughout. The text is suitable for a graduate course in analytic number theory.

Analytic Number Theory, Approximation Theory, and Special Functions

Gradimir V. Milovanović,Michael Th. Rassias
Analytic Number Theory Approximation Theory and Special Functions Book PDF

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 880 pages
File Size : 41,5 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Analytic Number Theory

Carl Pomerance,Michael Th. Rassias
Analytic Number Theory Book PDF

Author : Carl Pomerance,Michael Th. Rassias
Publisher : Springer
Page : 379 pages
File Size : 44,9 Mb
Release : 2015-11-18
Category : Mathematics
ISBN : 9783319222400

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Analytic Number Theory by Carl Pomerance,Michael Th. Rassias Pdf

This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

Analytic Number Theory

Jean-Marie De Koninck,Florian Luca
Analytic Number Theory Book PDF

Author : Jean-Marie De Koninck,Florian Luca
Publisher : American Mathematical Society
Page : 434 pages
File Size : 43,8 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781470473853

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Analytic Number Theory by Jean-Marie De Koninck,Florian Luca Pdf

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.

Topics in Analytic Number Theory

Hans Rademacher
Topics in Analytic Number Theory Book PDF

Author : Hans Rademacher
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642806155

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Topics in Analytic Number Theory by Hans Rademacher Pdf

At the time of Professor Rademacher's death early in 1969, there was available a complete manuscript of the present work. The editors had only to supply a few bibliographical references and to correct a few misprints and errors. No substantive changes were made in the manu script except in one or two places where references to additional material appeared; since this material was not found in Rademacher's papers, these references were deleted. The editors are grateful to Springer-Verlag for their helpfulness and courtesy. Rademacher started work on the present volume no later than 1944; he was still working on it at the inception of his final illness. It represents the parts of analytic number theory that were of greatest interest to him. The editors, his students, offer this work as homage to the memory of a great man to whom they, in common with all number theorists, owe a deep and lasting debt. E. Grosswald Temple University, Philadelphia, PA 19122, U.S.A. J. Lehner University of Pittsburgh, Pittsburgh, PA 15213 and National Bureau of Standards, Washington, DC 20234, U.S.A. M. Newman National Bureau of Standards, Washington, DC 20234, U.S.A. Contents I. Analytic tools Chapter 1. Bernoulli polynomials and Bernoulli numbers ....... . 1 1. The binomial coefficients ..................................... . 1 2. The Bernoulli polynomials .................................... . 4 3. Zeros of the Bernoulli polynomials ............................. . 7 4. The Bernoulli numbers ....................................... . 9 5. The von Staudt-Clausen theorem .............................. . 10 6. A multiplication formula for the Bernoulli polynomials ........... .