# [Liste-CICMA] Analytic Number Theory Seminar

Steve Lester sjlester at gmail.com
Mon Nov 21 09:54:05 EST 2016

Dear All,

This Thursday Sandro Bettin from the University of Genova  will be speaking
in the Analytic Number Theory Seminar from 2:00-3:30 in André Aisenstadt
(UdeM) room 5448 . Please find the title/abstract below.
Title: High moments of the Estermann function.

Abstract: For a rational number h/k, the Estermann function is defined as
the Dirichlet series $D(s,h/k)=\sum_{n\geq1} d(n) e^{2\pi n h/k} /n^s$ for
$\Re(s)>1$ and by meromorphic continuation in the rest of the complex
plane. We will show how to compute all moments of the Estermann function at
the central point s=1/2 when averaging  over h modulo k. In doing so we are
also led to the computation of the asymptotic with power saving error term
for the number of points in the projective variety x_0y_0+\cdots+x_ky_k=0.

Kind regards,
Steve Lester
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