2022

Regular poles for the p-adic group GSp4 -II

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

We compute the regular poles of the L-factors of the admissible and irreducible representations of the group GSp4 , which admit a nonsplit Bessel functional and have a Jacquet module length of 3 with respect to the unipotent radical of the Siegel parabolic, over a non-Archimedean local field of odd characteristic. We also compute the L-factors of the generic representations of GSp4 .

PDF

___

[1] Bump D. Automorphic Forms and Representations. New York, NY, USA: Cambridge Studies in Advanced Mathematics, 1998.
[2] Danı¸sman Y. Regular poles for the p-adic group GSp4 . Turk J Math 2014; 38: 587613.
[3] Gan W, Takeda S. The local Langlands conjecture for GSp(4). Ann Math 2011; 173: 18411882.
[4] Novodvorsky M. Automorphic L-functions for the symplectic group GSp(4). P Sympos Pure Math 1977; 33: 8795.
[5] Piatetski-Shapiro I. L-functions for GSp4 . Pacific J Math Olga Taussky Todd Memorial Issue 1997; 259275.
[6] Prasad D, Takloo-Bighash R. Bessel models for GSp(4). J Reine Angew Math 2011; 655: 189243.
[7] Roberts B, Schmidt R. New Forms for GSp(4). Springer Lecture Notes in Mathematics 1918. Heidelberg, Germany: Springer-Verlag, 2007.
[8] Sally PJ Jr, Tadic M. Induced representations and classifications for GSp(2, F) and Sp(2, F). Memoires Societe Mathematique de France 1993; 52: 75133.
[9] Shahidi F. A proof of Langlands conjecture on plancherel measures; complementary series for p-adic groups. Ann Math 1990; 132: 273330.
[10] Shahidi F. Eisenstein Series and Automorphic L-Functions. American Mathematical Society Colloquium Publications, Vol. 58. Providence, RI, USA: American Mathematical Society, 2010.
[11] Takloo-Bighash R. L-functions for the p-adic group GSp(4). Am J Math 2000; 122: 10851120.
[12] Tunnell J. Local L-factors and characters of GL(2). Am J Math 1983; 105: 12771307.