An introduction to probabilistic number theory
Author(s)
Bibliographic Information
An introduction to probabilistic number theory
(Cambridge studies in advanced mathematics, 192)
Cambridge University Press, 2021
- : hardback
Related Bibliography 1 items
Available at 30 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||CSAM||192200041773308
Note
Includes bibliographical references (p. 246-251) and index
Description and Table of Contents
Description
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
Table of Contents
- 1. Introduction
- 2. Classical probabilistic number theory
- 3. The distribution of values of the Riemann zeta function, I
- 4. The distribution of values of the Riemann zeta function, II
- 5. The Chebychev bias
- 6. The shape of exponential sums
- 7. Further topics
- Appendix A. Analysis
- Appendix B. Probability
- Appendix C. Number theory
- References
- Index.
by "Nielsen BookData"