منابع مشابه
On 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...
متن کاملOn the Lower Central Series of Pi-algebras
In this paper we study the lower central series {Li}i≥1 of algebras with polynomial identities. More specifically, we investigate the properties of the quotients Ni = Mi/Mi+1 of successive ideals generated by the elements Li. We give a complete description of the structure of these quotients for the free metabelian associative algebra A/(A[A,A][A,A]). With methods from Polynomial Identities the...
متن کاملOn 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).
متن کاملOn Exponential Sums with Hecke Series at Central Points
(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 Moments of Hecke Series at Central Points
We prove, in standard notation from spectral theory, the following asymptotic formulas:
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1962
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500014772