arXiv subjects

Samuel Estala Arias

Publications and source records attributed to Samuel Estala Arias.

2 recordsLinked to original sources

arXiv2017

A Heat Equation on some Adic Completions of Q and Ultrametric Analysis

This article deals with a Markov process related to the fundamental solution of a heat equation on the direct product ring Q_S, where Q_S is a finite direct product of p-adic fields. The techniques developed here are different from the well known ones: they are geometrical and very simple. As a result, the techniques developed here provides a general framework of these problems on other related ultrametric groups.

math.FA↗

arXiv2011

Distribution of cusp sections in the Hilbert modular orbifold

Let K be a number field, let M be the Hilbert modular orbifold of K, and let m(q) be the probability measure uniformly supported on the cusp cross sections of M at height q. We generalize a method of Zagier and show that m(q) distributes uniformly with respect to the normalized Haar measure m on M as q tends to zero, and relate the rate by which m(q) approaches m to the Riemann hypothesis for the Dedekind zeta function of K.

math.NT↗