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Abstract
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Studying the analytic properties of the partial Langlands
-function
via Rankin–Selberg method has proved to be successful in various cases. Yet in few
cases is the local theory studied at the archimedean places, which causes a
tremendous gap in the completion of the analytic theory of the complete
-function. We
establish the meromorphic continuation and the functional equation of the archimedean local
integrals associated with D. Ginzburg’s global integral (1991) for the adjoint representation
of
.
Via the local functional equation, the local gamma factor
can
be defined. In a forthcoming paper, we will compute the local gamma factor
explicitly, which fill in some blanks in the archimedean local theory of Ginzburg’s
global integral.
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Keywords
archimedean local integral, Rankin–Selberg integral,
adjoint L-function for general linear group
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Mathematical Subject Classification 2010
Primary: 22E45, 22E50
Secondary: 11F70
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Milestones
Received: 8 January 2018
Revised: 29 November 2018
Accepted: 13 March 2019
Published: 18 January 2020
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