An introduction to probabilistic number theory

著者

• Kowalski, Emmanuel

書誌事項

An introduction to probabilistic number theory

Emmanuel Kowalski

（Cambridge studies in advanced mathematics, 192）

Cambridge University Press, 2021

• : hardback

注記

Includes bibliographical references (p. 246-251) and index

内容説明・目次

内容説明

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.

目次

• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BC07267142
• ISBN:
  • 9781108840965
• LCCN: 2021002811
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge, U.K.
• ページ数/冊数: xiv, 255 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA241.7
  • DC23 : 512.7/6
• 件名:
  • LCSH : Probabilistic number theory
• 親書誌ID:
  • BA00109761