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

Hung Bui, A. Florea, J. P. Keating, E. Roditty-Gershon

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Abstract

We calculate the first and second moments of L–functions in the family of quadratic twists of a fixed elliptic curve E over Fq[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.
Original languageEnglish
Pages (from-to)1853-1893
Number of pages41
JournalAlgebra and Number Theory
Volume14
Issue number7
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Correlation
  • Elliptic curve
  • Finite field
  • L-function
  • Rank

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