Kernels of L-functions and shifted convolutions

TL;DR

This paper characterizes the field containing quotients of L-function values linked to cusp forms, using shifted convolution series and advanced modular value techniques to deepen understanding of these special functions.

Contribution

It introduces a novel characterization of the field of L-function quotients by combining shifted convolution series with multiple modular value methods.

Findings

Identifies the field containing L-function quotients.

Connects shifted convolution series with modular value techniques.

Provides new insights into the algebraic properties of L-values.

Abstract

We give a characterisation of the field into which quotients of values of L-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and to establish it we combine parts of F. Brown's technique to study multiple modular values with the properties of a double Eisentein series previously studied by the author and C. O'Sullivan.