Birkhäuser Advanced Texts Basler Lehrbücher
cover

Excursions in Multiplicative Number Theory

Authors: Ramaré, Olivier

  • Offers a unique exploration of analytic number theory that focuses on proving explicit bounds in cases suited to versatile tools
  • Emphasizes a methodological approach to the material with several different pathways to proceed
  • Promotes an active learning style with nearly 300 exercises appearing throughout
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eBook 58,84 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: January 14, 2022
  • ISBN 978-3-030-73169-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 72,79 €
price for Spain (gross)
  • Due: January 14, 2022
  • ISBN 978-3-030-73168-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

Olivier Ramaré is a Research Director at Aix Marseille Université in Marseille, France. He is a prolific researcher with a focus on sieve theory, prime numbers, the Möbius function, L-series, and more.

Buy this book

eBook 58,84 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • Due: January 14, 2022
  • ISBN 978-3-030-73169-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover 72,79 €
price for Spain (gross)
  • Due: January 14, 2022
  • ISBN 978-3-030-73168-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Excursions in Multiplicative Number Theory
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2021
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-73169-4
DOI
10.1007/978-3-030-73169-4
Hardcover ISBN
978-3-030-73168-7
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XXII, 336
Number of Illustrations
9 illustrations in colour
Topics