Whittaker Fourier type solutions to differential equations arising from string theory

TL;DR

This paper derives Fourier expansions for generalized Eisenstein series related to string theory, linking boundary conditions to divisor function convolutions and exploring connections with differential Galois theory.

Contribution

It provides explicit Fourier solutions for non-holomorphic Eisenstein series and connects these to divisor functions and differential Galois theory, advancing understanding in mathematical physics.

Findings

Explicit Fourier expansions for Eisenstein series.

Connection between boundary conditions and divisor function convolutions.

Potential links to differential Galois theory.

Abstract

In this article, we find the full Fourier expansion for the generalized non-holomorphic Eisenstein series for certain values of parameters. We give a connection of the boundary condition on such Fourier series with convolution formulas on the divisor functions. Additionally, we discuss a possible relation with the differential Galois theory.