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On arithmetic progressions on Edwards curves

Enrique González-Jiménez (2015)

Acta Arithmetica

Let m ∈ ℤ > 0 and a,q ∈ ℚ. Denote by m ( a , q ) the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve E d : x ² + y ² = 1 + d x ² y ² . We study the set m ( a , q ) and we parametrize it by the rational points of an algebraic curve.

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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