Number Theory Seminar

Selmer ranks of twists of hyperelliptic curves and superelliptic curves

Myungjun Yu, Graduate Student, Mathematics, UC Irvine,

Mazur and Rubin found sufficient conditions on an elliptic curve that it has infinitely many quadratic twists whose 2-Selmer ranks are equal to r for any non-negative integer r. We generalize this theorem to (Jacobian of) hyperelliptic curves and to (Jacobian of) superelliptic curves.

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For more information, please contact Pei-Yu Tsai by email at pytsai@caltech.edu or visit http://math.caltech.edu/~numbertheory/.