On the rank of quadratic twists of elliptic curvers over function fields

Details On the rank of quadratic twists of elliptic curvers over function fields On the rank of quadratic twists of elliptic curvers over function fields

2005-03-31

arxiv.org/abs/math/0503732v1

Mathematics

Number Theory

15 pages

Scientific paper

We prove quantitative upper bounds for the number of quadratic twists of a given elliptic curve $E/\Fp_q(C)$ over a function field over a finite field that have rank $\geq 2$, and for their average rank. The main tools are constructions and results of Katz and uniform versions of the Chebotarev density theorem for varieties over finite fields. Moreover, we conditionally derive a bound in some cases where the degree of the conductor is unbounded.

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