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Equidistribution in the dual group of the S -adic integers

Roman Urban (2014)

Czechoslovak Mathematical Journal

Let X be the quotient group of the S -adele ring of an algebraic number field by the discrete group of S -integers. Given a probability measure μ on X d and an endomorphism T of X d , we consider the relation between uniform distribution of the sequence T n 𝐱 for μ -almost all 𝐱 ∈ X d and the behavior of μ relative to the translations by some rational subgroups of X d . The main result of this note is an extension of the corresponding result for the d -dimensional torus 𝕋 d due to B. Host.

Estimating the critical determinants of a class of three-dimensional star bodies

Werner Georg Nowak (2017)

Communications in Mathematics

In the problem of (simultaneous) Diophantine approximation in  ℝ 3 (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body K 2 : ( y 2 + z 2 ) ( x 2 + y 2 + z 2 ) ≤ 1 play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant Δ ( K c ) of more general star bodies K c : ( y 2 + z 2 ) c / 2 ( x 2 + y 2 + z 2 ) ≤ 1 , where c is any positive constant. These are obtained by inscribing into K c either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of c .

Étude de L ( s , χ ) / π s pour des fonctions L relatives à 𝔽 q ( ( T - 1 ) ) et associées à des caractères de degré 1

Gilles Damamme (1999)

Journal de théorie des nombres de Bordeaux

Carlitz a défini pour les corps de fonctions l’analogue du réel π et Goss l’analogue des fonctions L de Dirichlet. Nous prouvons dans un cas particulier qu’il existe des valeurs entières s et des caractères χ pour lesquels L ( s , χ ) / π 8 peut être rationnel, algébrique ou bien transcendant.

Currently displaying 441 – 460 of 1536