23. Oct 2024

Negative moments of the Riemann zeta function

Datum: 23. October 2024 | 14:00 – 16:00
Sprecher: Alexandra Florea, UCI
Veranstaltungsort: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Sprache: Englisch

I will talk about the negative moments of the Riemann zeta function, both continuous and discrete, based on joint works with Bui, Keating and Milinovich. I will explain how to obtain progress towards a conjecture of Gonek on negative moments, when the shift of the negative zeta function is "small" (going to 0 with t). When we are integrating from T to 2T, and the shift is less than 1/(log T), we also discuss some conjectures based on random matrix theory and some heuristic number theoretic arguments which predict certain transition regimes in the asymptotic formulas.