Moments of elliptic integrals and critical $L$-values
Number Theory
2013-04-17 v2
Abstract
We compute the critical -values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral . In doing so, we prove closed form formulas for some moments of . Many of our -values can be expressed in terms of Gamma functions, and this also gives new lattice sum evaluations.
Cite
@article{arxiv.1303.2259,
title = {Moments of elliptic integrals and critical $L$-values},
author = {M. Rogers and J. G. Wan and I. J. Zucker},
journal= {arXiv preprint arXiv:1303.2259},
year = {2013}
}