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Journal of Number Theory
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Journal of Number Theory
Article . 1995
License: Elsevier Non-Commercial
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Journal of Number Theory
Article . 1995 . Peer-reviewed
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On Eisenstein Series of GLn

On Eisenstein series of \(GL_ n\)
Authors: Kim, D.S.;

On Eisenstein Series of GLn

Abstract

Since the results are very technical it is difficult to state them here explicitly and so we quote from the author's introduction: ``In this paper we present a new method of obtaining an analytic continuation and explicit functional equation for an Eisenstein series attached to any standard maximal parabolic subgroup of \(GL_ n\). One main idea of this work is that if we assume that there are at least two infinite places then we can introduce suitable Schwartz-Bruhat functions at infinity places which enable us to apply the usual Poisson summation formula. This method yields a very symmetric looking functional equation of our Eisenstein series attached to any standard maximal parabolic subgroup of \(GL_ n\). Aside from the above main idea this article is mostly computational in the spirit of Tate's thesis''.

Related Organizations
Keywords

analytic continuation, Algebra and Number Theory, Eisenstein series, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Schwartz-Bruhat functions, Other groups and their modular and automorphic forms (several variables), Poisson summation formula, functional equation, standard maximal parabolic subgroup of \(GL_ n\)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
hybrid