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

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arxiv 1902.00568 v1 pith:YUO5QF24 submitted 2019-02-01 math.NT

H. M. Bui , Alexandra Florea , Jonathan P. Keating , Edva Roditty-Gershon This is my paper · ORCID
classification math.NT
keywords twistsl-functionsmomentsquadraticcurveellipticanalyticasymptotically
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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.

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  1. Moments of Dirichlet $L$-functions with prime conductors over function fields

    math.NT 2019-09 conditional novelty 7.0 of 10

    For prime conductors over F_q[x], the paper obtains the g^2 term in the second moment of quadratic Dirichlet L-functions and the leading term in the mean derivative of elliptic-curve twists, implying a rank-one twist exists.

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