Shifted convolution sums and Eisenstein series formed with modular symbols

TL;DR

This paper explores the Fourier coefficients of second order Eisenstein series, expressing them as shifted convolution sums, and uses this to derive spectral decompositions and estimates for these sums.

Contribution

It introduces a novel approach to analyze second order Eisenstein series through shifted convolution sums, providing new spectral decomposition techniques.

Findings

Spectral decomposition of shifted convolution sums obtained

Estimates for the sums derived

Fourier coefficients expressed as shifted convolution sums

Abstract

The Fourier coefficient of a second order Eisenstein series is described as a shifted convolution sum. This description is used to obtain the spectral decomposition of and estimates for the shifted convolution sum.