Introduction To Analytic And Probabilistic Number Theory

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An Introduction To Probabilistic Number Theory

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Author : Emmanuel Kowalski
language : en
Publisher: Cambridge University Press
Release Date : 2021-05-06

An Introduction To Probabilistic Number Theory written by Emmanuel Kowalski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-06 with Mathematics categories.

This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.

Analytic Number Theory An Introductory Course

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Author : Paul Trevier Bateman
language : en
Publisher: World Scientific
Release Date : 2004-09-07

Analytic Number Theory An Introductory Course written by Paul Trevier Bateman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-07 with Mathematics categories.

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 www.math.uiuc.edu/~diamond/.

A Primer Of Analytic Number Theory

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Author : Jeffrey Stopple
language : en
Publisher: Cambridge University Press
Release Date : 2003-06-23

A Primer Of Analytic Number Theory written by Jeffrey Stopple and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-23 with Mathematics categories.

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.

Introduction To Analytic Number Theory

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Author : Tom M. Apostol
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Introduction To Analytic Number Theory written by Tom M. Apostol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

"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

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Author : Gérald Tenenbaum
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-26

Introduction To Analytic And Probabilistic Number Theory written by Gérald Tenenbaum and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-26 with Mathematics categories.

This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics. Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems. This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on up-to-date bibliography. The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate. —Mathematical Reviews

Analytic Number Theory

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Author : Jean-Marie De Koninck
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-31

Analytic Number Theory written by Jean-Marie De Koninck and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.

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.

Analytic And Elementary Number Theory

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Author : Krishnaswami Alladi
language : en
Publisher: Springer
Release Date : 2013-12-21

Analytic And Elementary Number Theory written by Krishnaswami Alladi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.

This volume contains a collection of papers in Analytic and Elementary Number Theory in memory of Professor Paul Erdös, one of the greatest mathematicians of this century. Written by many leading researchers, the papers deal with the most recent advances in a wide variety of topics, including arithmetical functions, prime numbers, the Riemann zeta function, probabilistic number theory, properties of integer sequences, modular forms, partitions, and q-series. Audience: Researchers and students of number theory, analysis, combinatorics and modular forms will find this volume to be stimulating.

Introduction To Analytic And Probabilistic Number Theory

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Author : G. Tenenbaum
language : en
Publisher: Cambridge University Press
Release Date : 1995-06-30

Introduction To Analytic And Probabilistic Number Theory written by G. Tenenbaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-30 with Mathematics categories.

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.

Steps Into Analytic Number Theory

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Author : Paul Pollack
language : en
Publisher: Springer Nature
Release Date : 2021-02-08

Steps Into Analytic Number Theory written by Paul Pollack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-08 with Mathematics categories.

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.

Ten Lectures On The Interface Between Analytic Number Theory And Harmonic Analysis

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Author : Hugh L. Montgomery
language : en
Publisher: American Mathematical Soc.
Release Date :

Ten Lectures On The Interface Between Analytic Number Theory And Harmonic Analysis written by Hugh L. Montgomery and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This book 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 valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent 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.