Overview
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses.Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Full Product Details
Author: Olivier Bordellès ,
Véronique Bordellès
Publisher: Springer Nature Switzerland AG
Imprint: Springer Nature Switzerland AG
Edition: 2nd ed. 2020
Weight: 1.211kg
ISBN: 9783030549459
ISBN 10: 3030549453
Pages: 782
Publication Date: 27 November 2020
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
Long chapters with many (exciting) subsections. There are a lot of problems to do (and, yes, do them); there are hints and answers in the back. The book is very well-written, doing a lot of deep stuff in detail and continually providing discussions of recent results, open questions, and so on. There are fantastic lists of references after each chapter. ... It's a wonderful book. (Michael Berg, MAA Reviews, January 30, 2022)
Author Information
Olivier Bordellès has been an independent researcher in number theory for 15 years, essentially working in multiplicative number theory and the links between algebraic number theory and analytic number theory. Véronique Bordellès is an English teacher who has translated several books in maths and science. She holds a BA in linguistics from the University of Manchester (UK) and also completed a Master's thesis in linguistics.
