Introduction To Analytic And Probabilistic Number Theory
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An Introduction to Probabilistic Number Theory
Author: Emmanuel Kowalski
language: en
Publisher: Cambridge University Press
Release Date: 2021-05-06
This introductory textbook for graduate students presents modern developments in probabilistic number theory, many for the first time.
Analytic Number Theory: An Introductory Course
Author: Paul Trevier Bateman
language: en
Publisher: World Scientific
Release Date: 2004-09-07
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
Author: Jeffrey Stopple
language: en
Publisher: Cambridge University Press
Release Date: 2003-06-23
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.