Trace formula on the p-adic upper half-plane

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Abstract

This article aims at showing a p-adic analogue of Selberg's trace formula, which describes a duality between the spectrum of a Hilbert-Schmidt operator and the length of prime geodesics appearing in the p-adic upper half-plane associated with a hyperbolic discontinuous subgroup of SL(2,Qp). Then we construct Markov processes on the fundamental domain relative to such subgroups, to whose transition operators the trace formula applied and a p-adic analogue of prime geodesic theorem is proved.

Original languageEnglish
Pages (from-to)422-454
Number of pages33
JournalJournal of Functional Analysis
Volume216
Issue number2
DOIs
Publication statusPublished - 2004 Nov 15
Externally publishedYes

Keywords

  • Ihara zeta function
  • Markov process
  • Prime geodesic theorem
  • Trace formula
  • p-Adic field

ASJC Scopus subject areas

  • Analysis

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