TEST VECTORS FOR ARCHIMEDEAN PERIOD INTEGRALS
- 주제(키워드) archimedean newform theory , archimedean Rankin-Selb erg integral , local and global period integrals , test vectors
- 주제(기타) Mathematics
- 설명문(일반) [Humphries, Peter] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA; [Jo, Yeongseong] Ewha Womans Univ, Dept Math Educ, Seoul 03760, South Korea
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 UNIV AUTONOMA BARCELONA
- 발행년도 2024
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000213867
- 본문언어 영어
- Published As https://doi.org/10.5565/PUBLMAT6812407
초록/요약
We study period integrals involving Whittaker functions associated to generic irreducible Casselman-Wallach representations of GLn(F), where F is an archimedean local field. Via the archimedean theory of newforms for GLn developed by the first author, we prove that newforms are weak test vectors for several period integrals, including the GLn x GLn Rankin-Selb erg 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-Selb erg periods, Flicker-Rallis periods, and Friedberg-Jacquet periods. These results parallel analogous results in the nonarchimedean setting proved by the second author, which use the nonarchimedean theory of newforms for GLn 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.
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