Central Values of $L$-Functions of Twisted Modular Forms and Local Polynomials

Charlotte Dombrowsky

Central Values of $L$-Functions of Twisted Modular Forms and Local Polynomials

Number Theory 2026-02-03 v1

Authors: Charlotte Dombrowsky

Abstract

In this paper we study the product of two central values of $L$ -functions of a twisted modular. We show that it suffices to compute a local polynomial at a finite number of points to decide whether the product is zero. For the proof, we relate the local polynomial to the product of the $L$ -functions using a locally harmonic Maass form and building on the Shimura-Shintani correspondence. This extends results from Ehlen, Guerzhoy, Kane and Rolen as well as Males, Mono, Rolen and Wagner.

Keywords

L-functions twisted modular forms central values local polynomials Shimura-Shintani correspondence

Cite

@article{arxiv.2602.01950,
  title  = {Central Values of $L$-Functions of Twisted Modular Forms and Local Polynomials},
  author = {Charlotte Dombrowsky},
  journal= {arXiv preprint arXiv:2602.01950},
  year   = {2026}
}

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