English

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 Γ0(N){\Gamma}_0(N) 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.

Keywords

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}
}