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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 $$> 1$$
##### Keywords:
twists; superelliptic curves; Mordell-Weil rank; Selmer rank
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