Excursions in Multiplicative Number Theory

Excursions in Multiplicative Number Theory

Author: Olivier Ramaré

Publisher: Birkhäuser

ISBN: 3030731685

Category: Mathematics

Page: 333

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This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three hundred exercises, making this an indispensable resource for both students and instructors. Designed to allow readers several different pathways to progress from basic notions to active areas of research, the book begins with a study of arithmetic functions and notions of arithmetical interest. From here, several guided “walks” invite readers to continue, offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. Having followed any one of the walks, readers will arrive at “higher ground”, where they will find opportunities for extensions and applications, such as the Selberg formula, Brun’s sieve, and the Large Sieve Inequality. Methodology is emphasized throughout, with frequent opportunities to explore numerically using computer algebra packages Pari/GP and Sage. Excursions in Multiplicative Number Theory is ideal for graduate students and upper-level undergraduate students who are familiar with the fundamentals of analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques in this active area.
Excursions in Multiplicative Number Theory
Language: en
Pages: 333
Authors: Olivier Ramaré
Categories: Mathematics
Type: BOOK - Published: 2022-01-24 - Publisher: Birkhäuser

This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three
Excursions in Multiplicative Number Theory
Language: en
Pages: 342
Authors: Olivier Ramaré
Categories: Electronic books
Type: BOOK - Published: 2021 - Publisher: Springer Nature

This textbook offers a unique exploration of analytic number theory that is focused on explicit and realistic numerical bounds. By giving precise proofs in simplified settings, the author strategically builds practical tools and insights for exploring the behavior of arithmetical functions. An active learning style is encouraged across nearly three
Multiplicative Number Theory I
Language: en
Pages: 574
Authors: Hugh L. Montgomery, Robert C. Vaughan
Categories: Mathematics
Type: BOOK - Published: 2007 - Publisher: Cambridge University Press

A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Computational Excursions in Analysis and Number Theory
Language: en
Pages: 220
Authors: Peter Borwein
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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.
Excursions in the History of Mathematics
Language: en
Pages: 347
Authors: Israel Kleiner
Categories: Mathematics
Type: BOOK - Published: 2012-02-02 - Publisher: Springer Science & Business Media

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four