Adam Harper: The Square of the Riemann Zeta Function Gives Rise...(September 11, 2025)

The Square of the Riemann Zeta Function Gives Rise to Critical Multiplicative Chaos ~ Multiplicative chaos is a class of random measures that have recently been found to have strong connections with number theoretic objects like L-functions and character sums and the phenomenon of “better than square-root cancellation.” Saksman and Webb have conjectured that integrating test functions against absolute powers of the Riemann zeta function should give rise to these measures. The square of the zeta function is particularly interesting, since this should correspond to the so-called critical chaos. Adam Harper will report on joint work (in preparation) with Saksman and Webb, which proves their conjecture for zeta squared. Harper will try to give a gentle introduction to these problems, and indicate some of the main proof ideas, which may be of independent interest. Uploaded 25-09-25 For more information go here: https://www.simonsfoundation.org/event/mps-conference-on-universal-statistics-in-number-theory/