This note complements a recent paper of Chatzakos, Harcos and Kaneko . We use a Dirichlet style Prime Geodesic Theorem to improve the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the Selberg trace formula.
In this article, for a non degenerate singular phase, we reconsider a stationary phase formula of Heifetz in the non-Archimedean local field setting and give a motivic analogue using Cluckers-Loeser's motivic integration.
We show that the coefficients of a power series occurring in p-adic Fourier theory for 𝐐_p^2 have valuations that are given by an intriguing formula.
A graph is said positively multiplicative when its adjacency matrix $A$ embeds in a matrix algebra admitting a basis $\mathfrak{B}$ with nonnegative structure constants in which the matrix multiplication by $A$ coincides with $A$. The goal of this paper is to present basics on this notion and expose, through various simple examples, how it relates to highly non trivial problems like the combinatorial description of fusion rules, the determination of spectrum in Cayley graphs, the description of the minimal boundary of graded graphs or the study of random walks on alcove tilings.
Au cours de l’étude des frises de Coxeter, M. Cuntz a défini la notion de λ -quiddités et a soulevé le problème de l’étude de celles-ci sur certains sous-ensembles de ℂ . L’objectif de ce texte est de mener à bien cette étude dans le cas de quelques sous-groupes monogènes de ( ℂ , + ). On s’intéressera tout particulièrement aux cas des sous-groupes monogènes engendrés par k et par i k avec k ∈ ℕ .
