Moments of the Riemann Zeta Function

Moments of the Riemann Zeta Function

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Peter Humphries, Princeton University
Fine Hall 314

An important area of study in analytic number theory is the average behaviour of the Riemann zeta function on the critical line Re(s) = 1/2. I'll talk a bit about what we know so far, and how random matrix theory helps us predict even more. If time permits, I'll discuss how one can generalise this to the average behaviour of families of L-functions at the critical point s = 1/2.