An Introduction to Probabilistic Number Theory

Probabilistic number theory studies the many surprising interactions between whole numbers and the theory of random processes. This incisive textbook for beginning graduate students is the first to present and explain some of the most modern developments in the field, focusing on key examples and probabilistic ideas in the arguments.

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.