Kernels for products of L-functions

TL;DR

This paper introduces new Eisenstein series constructed via double sums, connecting their properties to values of L-functions outside the critical strip, and extends the kernel method for products of L-functions.

Contribution

It develops a novel class of Eisenstein series and explores their relation to non-critical L-function values, expanding the kernel approach for L-function products.

Findings

New Eisenstein series constructed with double sums

Connection established between these series and non-critical L-function values

Extended kernel method for products of L-functions

Abstract

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their non-holomorphic analogs and show their connection to values of L-functions outside the critical strip.