#### Vol. 14, No. 7, 2020

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

### Hung M. Bui, Alexandra Florea, Jonathan P. Keating and Edva Roditty-Gershon

Vol. 14 (2020), No. 7, 1853–1893
DOI: 10.2140/ant.2020.14.1853
##### Abstract

We calculate the first and second moments of $L$-functions in the family of quadratic twists of a fixed elliptic curve $E$ over ${\mathbb{𝔽}}_{q}\left[x\right]$, 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
elliptic curve, L-function, rank, finite field, correlation
Primary: 11M06
Secondary: 11M38