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On concentrated probabilities

Wojciech Bartoszek (1995)

Annales Polonici Mathematici

Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence g n ∈ G such that μ ∗ n ( g n A ) ≡ 1 for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power μ ∗ k has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...

On concentrated probabilities on non locally compact groups

Wojciech Bartoszek (1996)

Commentationes Mathematicae Universitatis Carolinae

Let G be a Polish group with an invariant metric. We characterize those probability measures μ on G so that there exist a sequence g n ∈ G and a compact set A ⊆ G with   μ * n ( g n A ) ≡ 1   for all n .

On the S-Euclidean minimum of an ideal class

Kevin J. McGown (2015)

Acta Arithmetica

We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...

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