The Laplace transform for a pair of the Hecke Z-functions

Author:

Sergey~Varbanets,~Yakov~Vorobyov

2010 Mathematics Subject Classification:

11M06, 44A15.

Keywords:

Dirichlet character, Hecke zeta-function, Kloosterman sum, Laplace transform.

Abstract:

For the sum of pairwise products of values Z_m\!\big(s;\!\frac{\delta_1}{\gamma},0\!\big)\!Z_m\!\big(s;0,\!\frac{\delta_2}{\gamma}\!\big) of the Hecke zeta-functions over the ring of Gaussian integers, we obtain a formula for the Laplace transform on the half-line.

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Vol. 10 (18), 2015