Twisted Kronecker series and periods of modular forms on $\Gamma_0(N)$
Number Theory
2024-04-10 v1
Abstract
We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series.
Cite
@article{arxiv.2404.06016,
title = {Twisted Kronecker series and periods of modular forms on $\Gamma_0(N)$},
author = {Clifford Blakestad and YoungJu Choie},
journal= {arXiv preprint arXiv:2404.06016},
year = {2024}
}