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Graduate Student Number Theory Learning Seminar

Topics in Analytic Continuation

Location:  zoom
Date & time: Tuesday, 09 February 2021 at 4:00PM - 5:00PM

Abstract: The principle of analytic continuation is fundamental to analytic number theory and especially to the theory of Dirichlet series.  Recent talks in the GNTS/LS have mentioned the analytic continuation of the Riemann zeta function, GL(2) L-functions, and GL(2) Rankin-Selberg convolutions.  In this talk, I'll deviate from this beaten path and sketch out three toy problems which illustrate other methods for producing analytic continuations of Dirichlet series (and some of the challenges that arise along the way).  Buzzwords: sieving with Dirichlet series, spectral expansion of automorphic forms, multiple Dirichlet series.

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