Lower order terms for the moments of symplectic and orthogonal families of L -functions

Abstract

We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet L -functions, L ( 1 / 2 , χ d ) , and also of the L -functions associated to quadratic twists of an elliptic curve over Q . In so doing, we are led to study determinants of binomial coefficients of the form det ( ( 2 k − i − λ k − i + 1 2 k − 2 j ) ) .