English

Linear relations between $L$-values of newforms and moments of elliptic $K$ integral

Number Theory 2025-09-30 v3 Classical Analysis and ODEs

Abstract

By systematically translating certain integrals involving moments of the elliptic integral into LL-values of modular forms on Γ1(4),Γ(4)\Gamma_1(4), \Gamma(4) and Γ1(8)\Gamma_1(8), and then utilizing relations among the critical LL-values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals.

Keywords

Cite

@article{arxiv.2509.19960,
  title  = {Linear relations between $L$-values of newforms and moments of elliptic $K$ integral},
  author = {Kam Cheong Au},
  journal= {arXiv preprint arXiv:2509.19960},
  year   = {2025}
}