On Exponential Sums with Hecke Series at Central Points
نویسنده
چکیده
(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 ( 1 2 ) replacing H j ( 1 2 ) are also considered. The above sum is conjectured to be ≪ε K3/2+ε, which is proved to be true in the mean square sense.
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