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arXiv · 1203.4647

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

Ian P. Goulden·Duc Khiem Huynh·Rishikesh·Michael O. Rubinstein
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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 $\det (\binom{2k-i-λ_{k-i+1}}{2k-2j})$.

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Ian P. Goulden, Duc Khiem Huynh, Rishikesh, Michael O. Rubinstein. 2012-06-15. Lower order terms for the moments of symplectic and orthogonal families of $L$-functions. https://arxiv.org/abs/1203.4647

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