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An invariant trace formula for rank one lattices
Author(s) -
Hoffmann Werner
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.1999.3212070106
Subject(s) - mathematics , trace (psycholinguistics) , invariant (physics) , congruence (geometry) , selberg trace formula , pure mathematics , rank (graph theory) , combinatorics , geometry , mathematical physics , philosophy , linguistics , riemann zeta function
We prove a non—adelic invariant trace formula for rank one lattices. Unlike Arthur's adelic invariant trace formula for groups of general rank, our formula applies to non—congruence lattices, too, and the geometric terms are made explicit. The contribution of the continuous spectrum to the trace is given in terms of certain generalized Hecke operators, and the convergence problem with this contribution is resolved.