Affiliation:
1. Institute of Mathematics Department of Integrative Biology BOKU Wien 1180 Vienna Austria
Abstract
Abstract
Following Friedlander & Iwaniec [FRIEDLANDER, J. B.—IWANIEC, H.: Summation formulae for coefficients of L-functions, Canad. J. Math. 57 (2005), 494—505], the objective of this note are the coefficients a
n
of the Dirichlet series for L(s, χ
1)L(s, χ
2)L(s, χ
3) where χ
1, χ
2, χ
3 are primitive Dirichlet characters with modules D
1, D
2, D
3. For
∑
n
≤
x
a
n
$\sum\limits_{n\le x}a_n$
, with x large, sharp asymptotics are established which are uniform in D
1, D
2, D
3. To this end, the modern method for the estimation of exponential sums, due to [HUXLEY, M. N.: Area, Lattice Points, and Exponential Sums, LMS Monographs, New Ser. 13, University Press, Oxford, 1996] and others, is applied with gain.
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