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

## TL;DR

This paper computes moments of L-functions for quadratic twists of elliptic curves over function fields, revealing insights into their analytic ranks and correlations.

## Contribution

It introduces new asymptotic formulas for moments of L-functions and their derivatives in the context of quadratic twists over function fields.

## Key findings

- First and second moments of L-functions are asymptotically computed.
- Lower bounds on correlations between ranks of different elliptic curves are established.
- Moments involving derivatives of L-functions are also analyzed.

## 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.