On exponential sums with Hecke series at central points
نویسندگان
چکیده
منابع مشابه
On 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...
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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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The purpose of this paper is to obtain a bound for sums of Hecke series in short intervals which, as a by-product, gives a new bound for Hj( 1 2 ). We begin by stating briefly the necessary notation and some results involving the spectral theory of the non-Euclidean Laplacian. For a competent and extensive account of spectral theory the reader is referred to Y. Motohashi’s monograph [13]. Let {...
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We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on elliptic curves. Subject Classification (2010) Primary 11L07, 11T23 Secondary 11G20
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2007
ISSN: 0208-6573
DOI: 10.7169/facm/1229619651