On the moments of Hecke series at central points II

Details On the moments of Hecke series at central points II On the moments of Hecke series at central points II

2003-05-13

arxiv.org/abs/math/0305178v3

Functiones et Approximatio XXXI(2003), 7-22

Mathematics

Number Theory

16 pages, TeX formatting improved

Scientific paper

We prove, in standard notation from spectral theory, the asymptotic formula
($B>0$) $$ \sum_{\kappa_j\le T}\alpha_j H_j(1/2) = ({T\over\pi})^2 - BT\log T +
O(T(\log T)^{1/2}), $$ 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 $O(T(\log T)^\epsilon)$.

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