TY - JOUR
T1 - Trace formula on the p-adic upper half-plane
AU - Yasuda, Kumi
N1 - Copyright:
Copyright 2004 Elsevier B.V., All rights reserved.
PY - 2004/11/15
Y1 - 2004/11/15
N2 - 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.
AB - 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.
KW - Ihara zeta function
KW - Markov process
KW - Prime geodesic theorem
KW - Trace formula
KW - p-Adic field
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U2 - 10.1016/j.jfa.2004.03.008
DO - 10.1016/j.jfa.2004.03.008
M3 - Article
AN - SCOPUS:4344699754
VL - 216
SP - 422
EP - 454
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -