Abstract We study the spectrum of the self-similar suspension flows of subshifts arising from primitive substitutions. We focus on the case where the substitution matrix has a Salem number α as dominant eigenvalue. We obtain a Hölder exponent for the spectral measures for points away from zero and belonging to the field ℚ(α). This...

Abstract In his famous paper [11], J. Franke has defined a certain finite filtration of the space of automorphic forms of a general reductive group, which captures most of its internal representation theory. The purpose of this paper is to provide several concrete examples of yet unexpected phenomena, which occur in the Franke filtration...

Abstract Denote by \({\cal K}_0^n\) the family of all closed convex sets A ⊂ ℝn containing the origin 0 ∈ ℝn. For \(A \in {\cal K}_0^n\) , its polar set is denoted...

Abstract This paper is concerned with the model-theoretic study of pairs (K, F) where K is an algebraically closed field and F is a distinguished subfield of K allowing extra structure. We study the basic model-theoretic properties of those pairs, such as quantifier elimination, model-completeness and saturated models. We also prove...

Abstract We study the étale fundamental group of a singular reduced connected curve defined over an algebraically closed field of an arbitrary prime characteristic. It is shown that when the curve is projective, the étale fundamental group is a free product of the étale fundamental group of its normalization with a free finitely generated...

Abstract Let ⪯ be a preorder on a monoid H with identity 1H and s be an integer ≥ 2. The ⪯-height of an element x ∈ H is the supremum of the integers k ≥ 1 for which there is a (strictly) ⪯-decreasing sequence x1, …, xk of ⪯-non-units of H with x1 = x, where u ∈ H is a ⪯-unit if u ⪯ 1H ⪯ u and a ⪯-non-unit otherwise. We say H is ⪯-artinian...