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SUMMARY:High moments of the Estermann function
DTSTART:20170222T141500
DTEND:20170222T151500
DTSTAMP:20260415T033921Z
UID:888a3dda531523a7a5932af786524c57578d7da08f7a82b67a00808f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Sandro Bettin (Università di Genova)\nAbstract: For a rationa
 l 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 me
 romorphic 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 as k goes to infinity among primes. In do
 ing so we are also led to the computation of the asymptotic with power sav
 ing error term for the number of points in the projective variety x_0y_0+.
 ..+x_m y_m=0.
LOCATION:CH B3 31
STATUS:CONFIRMED
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