David Ginzburg

functions for the orthogonal group

Introduction Basic data Support ideals Certain Jacquet functors Global theory Support ideals (II) Calculation of local factors Determination of

On a Conjecture of Jacquet, Lai, and Rallis: Some Exceptional Cases

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Some double coset decompositions

-factors (spherical case) Determination of

Global genericity of the descent and global integrals of Rankin-Selberg type and of Shimura type

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Coefficients of Gelfand-Graev Type, of Fourier-Jacobi Type, and Descent

-factors (spherical-Whittaker case) Bibliography.

On Certain Residual Representations

We provetwospectral identities. Thefirstonerelates therelative traceformulafor thespher- ical variety GSpin(4,3)/G2 with a weighted trace formula for GL2. The second relates a spherical variety pertaining to F4 to one of GSp(6). These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.