Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 71-91.

ENDOSCOPIC TRANSFER AND AUTOMORPHIC L-FUNCTIONS: THE CASE OF THE GENERAL SPIN GROUP AND THE TWISTED SYMMETRIC AND EXTERIOR SQUARE L-FUNCTIONS

Neven Grbac

Juraj Dobrila University of Pula, Zagrebačka 30, HR-52100 Pula, Croatia
e-mail: neven.grbac@unipu.hr

Abstract.   The endoscopic classification and the Langlands spectral theory are two approaches to the discrete spectrum of the group of adèlic points of a reductive linear algebraic group defined over a number field. The two points of view on the same object yield interesting consequences. In this paper, the case of the general spin group is considered. In that case, it is shown how the comparison of the two approaches implies that the twisted symmetric and exterior square complete automorphic L-functions associated to a cuspidal automorphic representation of the general linear group are holomorphic in the critical strip.

2020 Mathematics Subject Classification.   11F66, 11F70, 11F72, 22E55.

Key words and phrases.   Twisted symmetric and exterior square automorphic L-function, general spin group, automorphic representation, endoscopic classification, spectral decomposition, Langlands-Shahidi method.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/m8vqrt3n19

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