Abstract
AbstractFollowing 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 coefficientsanof the Dirichlet series forL(s,χ1)L(s,χ2)L(s,χ3) whereχ1,χ2,χ3are primitive Dirichlet characters with modulesD1,D2,D3. For∑n≤xan$\sum\limits_{n\le x}a_n$, withxlarge, sharp asymptotics are established which are uniform inD1,D2,D3. 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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