## Student Number Theory Seminar 2019-20

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12/2/19: Henry Twiss -- *Moments of Multiple Dirichlet L-Series*

**Abstract:** Understanding the analytic properties of zeta and L-functions is critical to algebraic number theory and in particular the Riemann Hypothesis. In the 1980's an idea emerged that studying averaging families of Dirichlet L-functions gives analytic information about the original family of L-functions. We consider a well-chosen averaging family and discuss conjectures regarding the asymptotic behavior of the family's moments, the implications these conjectures have for the Riemann Hypothesis, and the computation of polynomials attached to these conjectures using the theory of infinite dimensional Kac-Moody Lie algebras.