THE RIEMANN ZETA FUNCTION AND GAUSSIAN MULTIPLICATIVE CHAOS: STATISTICS ON THE CRITICAL LINE

16Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

We prove that if ω is uniformly distributed on [0, 1], then as T →∞, t → ζ(iωT + it + 1/2) converges to a nontrivial random generalized function, which in turn is identified as a product of a very well-behaved random smooth function and a random generalized function known as a complex Gaussian multiplicative chaos distribution. This demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos—the latter is known to be connected to various branches of modern probability theory and mathematical physics.

Cite

CITATION STYLE

APA

Saksman, E., & Webb, C. (2020). THE RIEMANN ZETA FUNCTION AND GAUSSIAN MULTIPLICATIVE CHAOS: STATISTICS ON THE CRITICAL LINE. Annals of Probability, 48(6), 2680–2754. https://doi.org/10.1214/20-AOP1433

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free