An Introduction to Probabilistic Number Theory
An Introduction to Probabilistic Number Theory
CAD$56.95
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.
- Provides an introduction to probabilistic number theory from scratch at a level suitable for beginning graduate students
- Contains the most up-to-date developments in probabilistic number theory that are not available in any other book
- Emphasizes the probabilistic aspects of the proofs, and probability theory language, highlighting how ideas from probability are useful to understand even arithmetic arguments
- Contains appendices reviewing the basic results in analysis, probability and number theory most commonly used in the text
Reviews & endorsements
‘an excellent resource for someone trying to enter the field of probabilistic number theory’ Bookshelf by Notices of the American Mathematical Society
‘The book contains many exercises and three appendices presenting the material from analysis, probability and number theory that is used. Certainly the book is a good read for a mathematicians interested in the interaction between probability theory and number theory. The techniques used in the book appear quite advanced to us, so we would recommend the book for students at a graduate but not at an undergraduate level.’ Jörg Neunhäuserer, Mathematical Reviews
‘The book is very well written - as expected by an author who has already contributed very widely used and important books - and certainly belongs to all libraries of universities and research institutes. It has all the attributes to make a classic textbook in this fascinating domain.’ Michael Th. Rassias, zbMATH
Product details
May 2021Hardback
9781108840965
250 pages
150 × 230 × 25 mm
0.55kg
Available
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.
