MOMENTS OF ELLIPTIC INTEGRALS AND CRITICAL L-VALUES

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 03 . Many of our L-values can be expressed in terms of Gamma functions, and this also gives new lattice sum evaluations.