Arthur trace formula

E865100
analytic tool in number theory generalization of the Selberg trace formula trace formula

The Arthur trace formula is a far-reaching generalization of the Selberg trace formula that provides a powerful analytic tool for studying automorphic representations and establishing instances of the Langlands program.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form Occurrences
the Arthur trace formula 1

Statements (47)

Predicate Object
instanceOf analytic tool in number theory ⓘ
generalization of the Selberg trace formula ⓘ
trace formula ⓘ
appliesTo automorphic representations ⓘ
reductive groups over global fields ⓘ
context adelic groups ⓘ
reductive algebraic groups over number fields ⓘ
developedBy James Arthur NERFINISHED ⓘ
field Langlands program NERFINISHED ⓘ
automorphic forms ⓘ
harmonic analysis on reductive groups ⓘ
number theory ⓘ
representation theory ⓘ
generalizes Selberg trace formula NERFINISHED ⓘ
hasAspect geometric side ⓘ
spectral side ⓘ
hasComponent global trace formula NERFINISHED ⓘ
local trace formula ⓘ
hasGoal comparison of automorphic spectra for different groups ⓘ
stabilization for use in endoscopic classification ⓘ
involves Arthur parameters ⓘ
Eisenstein series NERFINISHED ⓘ
Levi subgroups ⓘ
characters of automorphic representations ⓘ
continuous spectrum ⓘ
discrete spectrum ⓘ
endoscopy ⓘ
intertwining operators ⓘ
orbital integrals ⓘ
parabolic subgroups ⓘ
stabilization ⓘ
truncation operators ⓘ
weighted orbital integrals ⓘ
namedAfter James Arthur NERFINISHED ⓘ
relatedTo Arthur–Selberg trace formula NERFINISHED ⓘ
Langlands functoriality NERFINISHED ⓘ
automorphic L-functions ⓘ
endoscopic transfer ⓘ
stable trace formula ⓘ
timePeriod late 20th century ⓘ
usedFor classification of automorphic representations ⓘ
comparison of trace formulas ⓘ
establishing instances of functoriality ⓘ
establishing instances of the Langlands correspondence ⓘ
spectral decomposition of automorphic forms ⓘ
stabilization of trace formulas ⓘ
studying automorphic representations ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Selberg trace formula → inspired → Arthur trace formula ⓘ
Selberg trace formula → generalizedBy → Arthur trace formula ⓘ
Plancherel theorem for real reductive groups → isImportantFor → Arthur trace formula ⓘ
this entity surface form: the Arthur trace formula