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On arithmetic progressions on Edwards curves

Enrique González-Jiménez (2015)

Acta Arithmetica

Let m > 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 asymptotic density and uniformly distributed sequences

Ryszard Frankiewicz, Grzegorz Plebanek (1996)

Studia Mathematica

Assuming Martin's axiom we show that if X is a dyadic space of weight at most continuum then every Radon measure on X admits a uniformly distributed sequence. This answers a problem posed by Mercourakis [10]. Our proof is based on an auxiliary result concerning finitely additive measures on ω and asymptotic density.

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