Trace formula for \(p\)-adics
type: Item
instance of: scholarly article
title: Trace formula for \(p\)-adics
zbMATH Open document ID: 1044.11045
DOI: 10.1023/A:1014527724008
author: Witold Karwowski
author: Kumi Yasuda
author: S. Albeverio
published in: Acta Applicandae Mathematicae
publication date: 2002-06-09T00:00:00Z
review text: The famous Selberg trace formula relates the trace of the kernel of the Brownian motion, i.e., the heat kernel, of a compact Riemann surface with hyperbolic metric to geometric data parametrized by closed geodesics. In this paper, the upper half plane is replaced by the field of \(p\)-adic numbers and the Riemannian surface by the ball of radius 1, which can be interpreted as a quotient of the \(p\)-adic field, and the Brownian motion is replaced by a random walk. A formula similar to the Selberg trace formula is obtained.
reviewed by: Lizhen Ji
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 37A45
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1752510
zbMATH Keywords: trace formula
zbMATH Keywords: p-adics
zbMATH Keywords: random walks
zbMATH Keywords: diffusions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1752510