An Introduction to Probabilistic Number Theory (Hardcover) (ISBN-13: 9781108840965)

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.

Author: Emmanuel Kowalski
ISBN-10: 1108840965
ISBN-13: 9781108840965
Publisher: Cambridge University Press
Language: English
Published: 05/06/2021
Pages: 250
Format: Hardcover
Weight: 1.25lbs
Size: 9.00h x 6.00w x 0.75d

Review Citation(s):
Choice 03/01/2022