Refined Estimates for Exponential Sums and a Problem Concerning the Product of Three L -Series

This article deals with estimates for single exponential sums, combining tools from the classic Van der Corput’s theory with an ingredient from M. Huxley’s work. Further, a very precise way of balancing terms is applied with gain. The result obtained is used to derive asymptotic estimates for the coefficients of products of three Dirichlet L-series, as was initiated by Friedlander and Iwaniec (Can. J. Math. 57(3):494–505, 2005).