Averages of coefficients of a class of degree seven L-functions

Abstract

In this paper, we give a detailed proof of an asymptotic formula for averages of coefficients of a class of degree seven L-functions which can be factorized as a product of degree one and degree six L-functions. We can break the 3/4-barrier in the error term and get an explicit exponent 34−30785172+ε. Our proof relies on methods from the theory of exponential sums.