# Trace formula on the p-adic upper half-plane

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 language English 422-454 33 Journal of Functional Analysis 216 2 https://doi.org/10.1016/j.jfa.2004.03.008 Published - 2004 Nov 15 Yes

### Fingerprint

Trace Formula
Half-plane
Geodesic
Selberg Trace Formula
Subgroup
Transition Operator
Hilbert-Schmidt Operator
Analogue
Fundamental Domain
Markov Process
Duality
Theorem

### Keywords

• Ihara zeta function
• Markov process
• Prime geodesic theorem
• Trace formula

• Analysis

### Cite this

In: Journal of Functional Analysis, Vol. 216, No. 2, 15.11.2004, p. 422-454.

Research output: Contribution to journalArticle

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