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Group theory --- Automorphic forms. --- Formes automorphes. --- Trace formulas. --- Formules de trace. --- Representations of groups. --- Représentations de groupes. --- Automorphic forms --- Representations of groups --- Trace formulas --- Formulas, Trace --- Discontinuous groups --- Group representation (Mathematics) --- Groups, Representation theory of --- Automorphic functions --- Forms (Mathematics)

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Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.

Trace formulas. --- Geometry, Algebraic. --- Harmonic analysis. --- p-adic groups. --- Analyse harmonique (mathématiques) --- Groupes p-adiques. --- Lie groups. --- Lie, Groupes de. --- Formules de trace. --- Trace formulas --- Geometry, Algebraic --- Algebraic geometry --- Geometry --- Formulas, Trace --- Automorphic forms --- Discontinuous groups --- Representations of groups

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"We study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank 2 over any algebraic number field. In particular, we express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke L-functions, and the Shintani zeta function for the space of binary quadratic forms."--

Selberg trace formula. --- Trace formulas. --- Geometry, Algebraic. --- Symplectic groups. --- Formule de trace de Selberg --- Formules de trace --- Géométrie algébrique --- Groupes symplectiques --- Selberg, Formule de trace de --- Selberg trace formula --- Trace formulas --- Geometry, Algebraic --- Symplectic groups --- Functions, Zeta --- Number theory --- Riemann surfaces --- Groups, Symplectic --- Linear algebraic groups --- Algebraic geometry --- Geometry --- Formulas, Trace --- Automorphic forms --- Discontinuous groups --- Representations of groups --- Selberg, Formule de trace de. --- Formules de trace. --- Géométrie algébrique. --- Groupes symplectiques.