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TEST VECTORS FOR ARCHIMEDEAN PERIOD INTEGRALS
- Title
- TEST VECTORS FOR ARCHIMEDEAN PERIOD INTEGRALS
- Authors
- Humphries, Peter; Jo, Yeongseong
- Ewha Authors
- 조영성
- SCOPUS Author ID
- 조영성
- Issue Date
- 2024
- Journal Title
- PUBLICACIONS MATEMATIQUES
- ISSN
- 0214-1493
- Citation
- PUBLICACIONS MATEMATIQUES vol. 68, no. 1, pp. 139 - 185
- Keywords
- archimedean newform theory; archimedean Rankin-Selb erg integral; local and global period integrals; test vectors
- Publisher
- UNIV AUTONOMA BARCELONA
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- 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.
- DOI
- 10.5565/PUBLMAT6812407
- Appears in Collections:
- 사범대학 > 수학교육과 > Journal papers
- Files in This Item:
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