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On the arithmetic of the hyperelliptic curve y 2 = x n + a

Kevser Aktaş, Hasan Şenay (2016)

Czechoslovak Mathematical Journal

We study the arithmetic properties of hyperelliptic curves given by the affine equation y 2 = x n + a by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps).

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