The rank of hyperelliptic Jacobians in families of quadratic twists
نویسندگان
چکیده
The variation of the rank of elliptic curves over Q in families of quadratic twists has been extensively studied by Gouvêa, Mazur, Stewart, Top, Rubin and Silverberg. It is known, for example, that any elliptic curve over Q admits infinitely many quadratic twists of rank ≥ 1. Most elliptic curves have even infinitely many twists of rank ≥ 2 and examples of elliptic curves with infinitely many twists of rank ≥ 4 are known. There are also certain density results. This paper studies the variation of the rank of hyperelliptic Jacobian varieties in families of quadratic twists in an analogous way.
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