Triple Shifted Sums of Automorphic L-Functions

Abstract

In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic cusp forms. The foundations of this construction are based in the continuation of the spectral expansion of a special truncated Poincaré series recently developed by Jeffrey Hoffstein. As a result we are able to produce previously unstudied and nontrivial asymptotics of truncated shifted sums which we expect to correspond to off-diagonal terms in the third moment of automorphic L-functions.

Ph.D. Thesis for Brown University

Cited by in corpus (4)

• Subconvexity for Half Integral Weight $L$-functions
• Second Moments and simultaneous non-vanishing of GL(2) automorphic L-series
• A Shifted Sum for the Congruent Number Problem
• Shifted Multiple Dirichlet Series