Publications [#320416] of Jayce R. Getz

Papers Published

1. Getz, JR; Wambach, E, Twisted relative trace formulae with a view towards unitary groups, American Journal of Mathematics, vol. 136 no. 1 (January, 2014), pp. 1-57, Johns Hopkins University Press: American Journal of Mathematics
   (last updated on 2024/04/24)

   Abstract:
   We introduce a twisted relative trace formula which simultaneously generalizes the twisted trace formula of Langlands et. al. (in the quadratic case) and the relative trace formula of Jacquet and Lai [JL]. Certain matching statements relating this twisted relative trace formula to a relative trace formula are also proven (including the relevant fundamental lemma in the "biquadratic case"). Using recent work of Jacquet, Lapid and their collaborators [J1] and the Rankin-Selberg integral representation of the Asai L-function (obtained by Flicker using the theory of Jacquet, Piatetskii-Shapiro, and Shalika [Fl2]), we give the following application: Let E/F be a totally real quadratic extension, let U ' be a quasi-split unitary group with respect to a CM extension M/F, and let U := U'_E . Under suitable local hypotheses, we show that a cuspidal cohomological automorphic representation of U whose Asai L-function has a pole at the edge of the critical strip is nearly equivalent to a cuspidal cohomological automorphic representation 0 of U that is U '-distinguished in the sense that there is a form in the space of 0 admitting a nonzero period over U . This provides cohomologically nontrivial cycles of middle dimension on unitary Shimura varieties analogous to those on Hilbert modular surfaces studied by Harder, Langlands, and Rapoport [HLR].