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

Autor:	Goldfeld, Dorian, Stade, Eric, Woodbury, Michael
Rok vydání:	2023
Předmět:	Mathematics - Number Theory 11F55 11F72
Druh dokumentu:	Working Paper
Popis:	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 are short and simple, and use the Borel Eisenstein series as a template to determine the first Fourier coefficient of other Langlands Eisenstein series. Comment: arXiv admin note: text overlap with arXiv:2212.14534
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.05442 Zobrazit plný text záznamu View this record from Arxiv