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The trace formula and Hecke operators. (English) Zbl 0671.10026

Number theory, trace formulas and discrete groups, Symp. in Honor of Atle Selberg, Oslo/Norway 1987, 11-27 (1989).
[For the entire collection see Zbl 0661.00005.]
The first section of this paper presents a general view on the Selberg trace formula in invariant form. In the second one it is described how to work over the adèles to deal with congruence subgroups (the group SL(n) is taken as an example). By the way the effective method of truncation for invariant kernels is given.
In the last section the main achievement is exposed: the trace of Hecke operators as a finite closed formula (sometimes called “Arthur’s trace formula”).
Reviewer: N.V.Kuznetsov

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F06 Structure of modular groups and generalizations; arithmetic groups
11F11 Holomorphic modular forms of integral weight

Citations:

Zbl 0661.00005