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- Arthur–Selberg_trace_formula abstract "In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over global fields, developed by James Arthur in a long series of papers from 1974 to 2003. It describes the character of the representation of G(A) on the discrete part L20(G(F)∖G(A)) of L2(G(F)∖G(A)) in terms of geometric data, where G is a reductive algebraic group defined over a global field F and A is the ring of adeles of F.There are several different versions of the trace formula. The first version was the unrefined trace formula, whose terms depend on truncation operators and have the disadvantage that they are not invariant. Arthur later found the invariant trace formula and the stable trace formula which are more suitable for applications. The simple trace formula (Flicker & Kazhdan 1988) is less general but easier to prove. The local trace formula is an analogue over local fields.Jacquet's relative trace formula is a generalization where one integrates the kernel function over non-diagonal subgroups.".
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- Arthur–Selberg_trace_formula wikiPageWikiLinkText "Arthur–Selberg trace formula".
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- Arthur–Selberg_trace_formula subject Category:Automorphic_forms.
- Arthur–Selberg_trace_formula subject Category:Theorems_in_harmonic_analysis.
- Arthur–Selberg_trace_formula comment "In mathematics, the Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over global fields, developed by James Arthur in a long series of papers from 1974 to 2003.".
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