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, $L(1/2,{\chi }_d)$, 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 $\det ((\genfrac{}{}{0ex}{}{2k-i-{\lambda }_{k-i+1}}{2k-2j}))$.

34 pages, 4 tables

References in corpus (2)

• A Hybrid Euler-Hadamard product formula for the Riemann zeta function
• Combinatorics of lower order terms in the moment conjectures for the Riemann zeta function

Cited by in corpus (1)

• Combinatorics of lower order terms in the moment conjectures for the Riemann zeta function