Displaying 101 – 120 of 1144

Showing per page

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 Automorphisms of the Affine Cremona Group

Hanspeter Kraft, Immanuel Stampfli (2013)

Annales de l’institut Fourier

We show that every automorphism of the group 𝒢 n : = A u t ( 𝔸 n ) of polynomial automorphisms of complex affine n -space 𝔸 n = n is inner up to field automorphisms when restricted to the subgroup T 𝒢 n of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension n = 2 where all automorphisms are tame: T 𝒢 2 = 𝒢 2 . The methods are different, based on arguments from algebraic group actions.

Currently displaying 101 – 120 of 1144