Moments of elliptic integrals and critical L-values

2013/03/09 by Rogers, M., Wan, J. G., Zucker, I. J. · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1303.2259

Abstract

We compute the critical L-values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral K. In doing so, we prove closed form formulas for some moments of K'³. Many of our L-values can be expressed in terms of Gamma functions, and this also gives new lattice sum evaluations.

Cited by

• The Explicit Hypergeometric Modularity Method III
• Linear relations between L-values of newforms and moments of elliptic K integral

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