Details

Dorian Goldfeld ^[a], Stephen D. Miller ^[b] and Michael Woodbury ^[c]

A template method for Fourier coefficients of Langlands Eisenstein series

Pages: 63-117
Received: 24 March 2020
Accepted in revised form: 29 July 2020
Mathematics Subject Classification (2010): 11S40, 11F70, 11F30.
Keywords: Eisenstein series, Fourier coefficients, GL(n), Chevalley group.
Authors address:
[a],[c]: Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, USA
[b]: Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854-8019, USA

Miller was supported by NSF Grant DMS-1801417. Goldfeld was supported by Simons Collaboration Grant Number 567168.

Abstract: This paper introduces the template method for computing the first coefficient of Langlands Eisenstein series on \(GL(n,\mathbb R)\) and more generally on Chevalley groups over the adele ring of \(\mathbb Q.\) In brief, the first coefficient of Borel Eisenstein series can be used as a template to compute the first coefficient of more general Eisenstein series by elementary linear algebra calculations.

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