Excursions in Multiplicative Number Theory

This textbook provides a unique exploration of analytic number theory, focusing on explicit and realistic numerical bounds. It offers precise proofs in simplified settings and encourages an active learning style with nearly three hundred exercises. It begins with a study of arithmetic functions and notions of arithmetical interest and leads to explorations of the convolution method, Levin–Faĭnleĭb theorem, and Mellin transform. Methodology is emphasized throughout, and the book is ideal for graduate students and upper-level undergraduate students familiar with analytic number theory. It will also appeal to researchers in mathematics and engineering interested in experimental techniques.

Format: Hardback
Length: 338 pages
Publication date: 04 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook delves into the realm of analytic number theory, offering a unique and insightful exploration of the subject. By providing precise proofs in simplified settings, the author skillfully constructs practical tools and insights that facilitate the study of the behavior of arithmetical functions. An active learning approach is fostered through nearly three hundred engaging exercises, making this resource an invaluable asset for students and instructors alike.

The book is meticulously structured to cater to readers with varying levels of expertise, beginning with a comprehensive study of arithmetic functions and notions of arithmetical interest. From there, a series of guided "walks" are presented, each offering explorations along three broad themes: the convolution method, the Levin–Faĭnleĭb theorem, and the Mellin transform. By following any one of these walks, readers will gradually ascend to "higher ground," where they will discover numerous opportunities for extensions and applications, including the Selberg formula, the Bruns sieve, and the Large Sieve Inequality.

Methodology plays a central role throughout the text, with frequent opportunities for readers to explore numerically using computer algebra packages such as Pari/GP and Sage. This hands-on approach enhances the understanding and application of the theoretical concepts presented.

Excursions in Multiplicative Number Theory is particularly well-suited for graduate students and upper-level undergraduate students who possess a solid foundation in analytic number theory. It also appeals to researchers in mathematics and engineering who are interested in employing experimental techniques in this dynamic and active area of research.

In summary, this textbook provides a comprehensive and engaging exploration of analytic number theory, equipping readers with the necessary tools and knowledge to understand and analyze arithmetical functions in a variety of settings. Its active learning approach, coupled with practical numerical exploration, makes it an essential resource for students, researchers, and practitioners alike.

Weight: 771g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030731687
Edition number: 1st ed. 2022