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On the arithmetic of twists of superelliptic curves. (English) Zbl 1152.11026
Summary: We consider a family of twists of a superelliptic curve over a global field, and obtain results on the distribution of the Mordell-Weil rank of these twists. Our results have application to the distribution of the number of rational points.

MSC:
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
11G10 Abelian varieties of dimension \(> 1\)
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