On the moments of Hecke series at central points II

2003/05/31 by Aleksandar Ivic, Matti Jutila
Mathematics · #math.NT #msc:11F72 #msc:11F66 #msc:11M41 #msc:11M06

paper · pdf

published as Functiones et Approximatio XXXI(2003), 7-22 · 16 pages, TeX formatting improved

arxiv created 2003/11/06 · arxiv updated 2009/11/30

Abstract

We prove, in standard notation from spectral theory, the asymptotic formula (B>0) ∑_{κj≤ T}α_j H_j(1/2) = (T\overπ)² - BTlog T + O(T(log T)^1/2), by using an approximate functional equation for H_j(1/2) and the Bruggeman--Kuznetsov trace formula. We indicate how the error term may be improved to O(T(log T)^ε).

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