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THE DEGENERATE RESIDUAL SPECTRUM OF QUASI-SPLIT FORMS OF Spin8 ASSOCIATED TO THE HEISENBERG PARABOLIC SUBGROUP.
- Source :
-
Transactions of the American Mathematical Society . 11/1/2019, Vol. 372 Issue 9, p6703-6754. 52p. - Publication Year :
- 2019
-
Abstract
- In [J. Inst. Math. Jussieu 14 (2015), pp. 149-184] and [Int. Math. Res. Not. imrn 7 (2017), pp. 2014-2099], the twisted standard L-function L(s, π, χ, st) of a cuspidal representation π of the exceptional group of type G2 was shown to be represented by a family of new-way Rankin-Selberg integrals. These integrals connect the analytic behaviour of L(s, π, χ, st) with that of a family of degenerate Eisenstein series εE(χ, fs, s, g) on quasi-split forms HE of Spin8, induced from Heisenberg parabolic subgroups. The analytic behaviour of the series εE(χ, fs, s, g) in the right half-plane Re(s) > 0 was studied in [Tran. Amer. Math. Soc. 370 (2018), pp. 5983-6039]. In this paper we study the residual representations associated with EE(χ, fs, s, g). [ABSTRACT FROM AUTHOR]
- Subjects :
- *EISENSTEIN series
*MATHEMATICS
*L-functions
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 372
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 139467150
- Full Text :
- https://doi.org/10.1090/tran/7901