Moments of the Riemann zeta function
Nathan Ng (University of Lethbridge)
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
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 |