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

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 $\mathrm{SL}(n,\mathbb{Z})$ in an elementary manner, and then determine the first Fourier coefficient of these series in a very explicit form. Our proofs and derivations are short and simple, and use the Borel Eisenstein series as a template to determine the first Fourier coefficient of other Langlands Eisenstein series.

arXiv admin note: text overlap with arXiv:2212.14534

Cited by in corpus (1)

• The Functional Equations of Langlands Eisenstein Series for $SL(n,\mathbb{Z})$