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- W4226506656 abstract "We study period integrals involving Whittaker functions associated to generic irreducible Casselman-Wallach representations of $mathrm{GL}_n(F)$, where $F$ is an archimedean local field. Via the archimedean theory of newforms for $mathrm{GL}_n$ developed by the first author, we prove that newforms are weak test vectors for several period integrals, including the $mathrm{GL}_n times mathrm{GL}_n$ Rankin-Selberg integral, the Flicker integral, and the Bump-Friedberg integral. By taking special values of these period integrals, we deduce that newforms are weak test vectors for Rankin-Selberg periods, Flicker-Rallis periods, and Friedberg-Jacquet periods. These results parallel analogous results in the nonarchimedean setting proven by the second author, which use the nonarchimedean theory of newforms for $mathrm{GL}_n$ developed by Jacquet, Piatetski-Shapiro, and Shalika. By combining these archimedean and nonarchimedean results, we prove the existence of weak test vectors for certain global period integrals of automorphic forms." @default.
- W4226506656 created "2022-05-05" @default.
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- W4226506656 date "2021-12-13" @default.
- W4226506656 modified "2023-09-24" @default.
- W4226506656 title "Test Vectors for Archimedean Period Integrals" @default.
- W4226506656 hasPublicationYear "2021" @default.
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