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On the moments of Hecke series at central points II

Aleksandar Ivic·Matti Jutila
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Abstract

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

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Aleksandar Ivic, Matti Jutila. 2003-11-06. On the moments of Hecke series at central points II. https://arxiv.org/abs/math/0305178

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