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      The first coefficient of Langlands Eisenstein series for \(\hbox{SL}(n,\mathbb Z)\)

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          Abstract

          Fourier coefficients of Eisenstein series figure prominently in the study of automorphic L-functions via the Langlands-Shahidi method, and in various other aspects of the theory of automorphic forms and representations. In this paper, we define Langlands Eisenstein series for \({\rm SL}(n,\mathbb Z)\) in an elementary manner, and then determine the first Fourier coefficient of these series in a very explicit form. Our proofs and derivations of are short and simple, and use the Borel Eisenstein series as a template to determine the first Fourier coefficient of other Langlands Eisenstein series.

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          Author and article information

          Journal
          09 March 2023
          Article
          2303.05442
          32092dd9-3e78-4f13-ae3a-cedba921edcc

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          11F55, 11F72
          arXiv admin note: text overlap with arXiv:2212.14534
          math.NT

          Number theory
          Number theory

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