The Riemann Zeta Process
Event details
| Date | 27.10.2025 |
| Hour | 16:15 › 17:15 |
| Speaker | Mike Cranston (University of California Irvine) |
| Location |
CM 517
|
| Category | Conferences - Seminars |
| Event Language | English |
Abstract: A classical method for sampling a random integer Y(N) according to the uniform distribution on [0,N] is to use the Riemann zeta distribution on the integers. That is, a random integer X(s) is sampled with probability of being n equal to 1/\zeta(s)n^s, where s>1. Then the asymptotics of arithmetic functions of X(s) where s goes to 1 have been studied recently by myself, Peltzer, Mountford, Hsu and Khodiakova.
The results are always the same as when one evaluates the arithmetic function at Y(N) and lets N go to infinity. A question comes up as to whether one can define a natural process X(s) and whether such a process would shed any light on the nature of the integers being sampled. In this talk, we will discuss a natural method to produce such a process and explain its properties. This is joint work with Jingyuan Chen.
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