Moments of quadratic twists of elliptic curve L-functions over function fields
Number Theory
2020-08-26 v1
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.
Keywords
Cite
@article{arxiv.1902.00568,
title = {Moments of quadratic twists of elliptic curve L-functions over function fields},
author = {H. M. Bui and Alexandra Florea and Jonathan P. Keating and Edva Roditty-Gershon},
journal= {arXiv preprint arXiv:1902.00568},
year = {2020}
}
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32 pages