Moments of quadratic twists of elliptic curve L-functions over function fields

Abstract

We calculate the first and second moments of L-functions in the family of quadratic twists of a fixed elliptic curve E over F_q[x], asymptotically in the limit as the degree of the twists tends to infinity. We also compute moments involving derivatives of L-functions over quadratic twists, enabling us to deduce lower bounds on the correlations between the analytic ranks of the twists of two distinct curves.

arXiv comment32 pages

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• Non-vanishing for cubic $L$--functions
• Moments of quadratic Dirichlet $L$-functions over Function Fields
• Moments of Dirichlet $L$-functions to a fixed modulus over function fields
• The first moment of quadratic twists of modular $L$-functions