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

2012/03/20 by I. P. Goulden, Ian P. Goulden, Duc Khiem Huynh +6
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.CO #math.NT #msc:05E05 #msc:11M50

paper · pdf · doi:10.48550/arxiv.1203.4647

34 pages, 4 tables

arxiv created 2012/06/15 · arxiv updated 2012/06/18

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 (\binom2k-i-λ_k-i+12k-2j).

Related

• Multiple Dirichlet series predictions for moments of L-functions: unitary, symplectic and orthogonal examples
• Lower bounds for moments of L-functions: symplectic and orthogonal examples
• Sharp lower bounds for moments of quadratic Dirichlet L-functions
• Sharp upper bounds for moments of quadratic Dirichlet L-functions
• Conjectures and experiments concerning the moments of L(1/2,χ_d)