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 -values of modular forms on and , and then utilizing relations among the critical -values of cuspidal newforms, we obtain a dimension formula for the space spanned by these integrals.
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}
}