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Reps Seminar - David Soudry

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December 2, 2015
4:30PM - 5:30PM
Math Tower 154

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Add to Calendar 2015-12-02 16:30:00 2015-12-02 17:30:00 Reps Seminar - David Soudry Title: On Rankin-Selberg integrals for classical groupsSpeaker: David Soudry (Tel Aviv University, currently visiting Columbia University)Abstract: I will survey the structure of families of global integrals of Rankin-Selberg type, which were predicted to represent partial L-functions for pairs of irreducible, automorphic, cuspidal representations (\pi, \tau) on (G, GL_n), where G is a classical group. I will focus on split orthogonal groups. In the global integrals, we integrate a Fourier coefficient "of Bessel type" applied to a cusp form on G against an Eisenstein series on a related classical group H, induced from a maximal parabolic subgroup, or vice versa. These families of integrals contain all known ones which represent the partial L-functions above. They were first introduced by Ginzburg, Piatetski-Shapiro and Rallis, and were calculated in the so-called "spherical case" (of Bessel models). I will present the calculation of the unramified local integrals at all cases. It is done by "analytic continuation" from the generic cases above. The global integrals above are useful in locating poles of L-functions of representations \pi with a given type of Bessel models.Seminar URL: https://research.math.osu.edu/reps/ Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: On Rankin-Selberg integrals for classical groups

Speaker: David Soudry (Tel Aviv University, currently visiting Columbia University)

Abstract: I will survey the structure of families of global integrals of Rankin-Selberg type, which were predicted to represent partial L-functions for pairs of irreducible, automorphic, cuspidal representations (\pi, \tau) on (G, GL_n), where G is a classical group. I will focus on split orthogonal groups. In the global integrals, we integrate a Fourier coefficient "of Bessel type" applied to a cusp form on G against an Eisenstein series on a related classical group H, induced from a maximal parabolic subgroup, or vice versa. These families of integrals contain all known ones which represent the partial L-functions above. They were first introduced by Ginzburg, Piatetski-Shapiro and Rallis, and were calculated in the so-called "spherical case" (of Bessel models). I will present the calculation of the unramified local integrals at all cases. It is done by "analytic continuation" from the generic cases above. The global integrals above are useful in locating poles of L-functions of representations \pi with a given type of Bessel models.

Seminar URL: https://research.math.osu.edu/reps/

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