On the moments of Hecke series at central points
نویسندگان
چکیده
منابع مشابه
On the Moments of Hecke Series at Central Points Ii
We prove, in standard notation from spectral theory, the asymptotic formula (B > 0) ∑ κj≤T αjHj( 1 2 ) = ( T π ) 2 − BT log T +O(T (log T )), by using an approximate functional equation for Hj( 1 2 ) and the Bruggeman-Kuznetsov trace formula. We indicate how the error termmay be improved to O(T (log T )ε).
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We prove, in standard notation from spectral theory, the following asymptotic formulas:
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(T ε ≤ K ≤ T ) are considered, where αj = |ρj(1)| (coshπκj) , and ρj(1) is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue λj = κ 2 j + 1 4 to which the Hecke series Hj(s) is attached. The problem is transformed to the estimation of a classical exponential sum involving the binary additive divisor problem. The analogous exponential sums with Hj( 1 2 ) or H j...
متن کاملOn the Central Derivative of Hecke L-series
The well-known Birch and Swinnerton-Dyer conjecture gives a deep connection between the leading coefficient of the L-series and the arithmetic properties of an abelian variety. Both are very important and subtle. This paper is part of an effort to compute the analytic side explicitly in a special case. Indeed, we are interested in the central derivative of certain algebraic Hecke L-series, rela...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2002
ISSN: 0208-6573
DOI: 10.7169/facm/1538186661