Integral representations related to triple product L-functions

Jayce Getz
Duke university

Date(s) : 16/06/2022   iCal
14 h 00 min - 15 h 00 min

Triple product L-functions are the Langlands L-functions attached to a triple of automorphic representations of GL_{r_i} for positive integers r_1,r_2,r_3 and the tensor product representation GL_{r_1} \times GL_{r_2} \times GL_{r_3} \lto \GL_{r_1r_2r_3}.

If we knew their analytic properties then by the converse theorem one would be able to deduce the automorphy of Rankin-Selberg products of automorphic representations.  This corresponds to the special case r_3=1.   This in turn would make huge inroads into Langlands functoriality.  I will report on joint work with Pam Gu, Chun-Hsien Hsu, and Spencer Leslie in which we construct an integral representation related to triple product L-functions, generalizing work of Garrett, Piatetski-Shapiro, and Rallis in the case r_1=r_2=r_3=2.  I will also comment on the obstacles to using this integral representation to obtain the functional equation of triple product L-functions, and how one might overcome them.

Campus de Luminy, Marseille


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