Moments of the Riemann zeta function

Nathan Ng (University of Lethbridge)

07-Oct-2021, 22:30-23:30 (2 years ago)

Abstract: For over a 100 years, $I_k(T)$, the $2k$-th moments of the Riemann zeta function on the critical line have been extensively studied. In 1918 Hardy-Littlewood established an asymptotic formula for the second moment ($k=1$) and in 1926 Ingham established an asymptotic formula for the fourth moment $(k=2)$. Since then no other moments have been asymptotically evaluated. In the late 1990's Keating and Snaith gave a conjecture for the size of $I_k(T)$ based on a random matrix model. Recently I showed that an asymptotic formula for the sixth moment ($k=3$) follows from a conjectural formula for some ternary additive divisor sums. In this talk I will give an overview of these results.

algebraic geometrynumber theory

Audience: researchers in the topic


SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

Seminar usually meets in-person. For online editions, the Zoom link is shared via mailing list.

Organizers: Katrina Honigs*, Nils Bruin*
*contact for this listing

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