Fourier coefficients of Eisenstein series of degree 3
type: Item
instance of: scholarly article
title: Fourier coefficients of Eisenstein series of degree 3
zbMATH Open document ID: 0551.10024
author: Yoshiyuki Kitaoka
published in: Proceedings of the Japan Academy. Series A
publication date: 1984-01-01T00:00:00Z
review text: The paper gives explicit formulas for the Fourier coefficients \(a_ k(T)\) of Eisenstein series of degree 3 and even weight k. By Siegel's works on Eisenstein series, \(a_ k(T)\) can be expressed as a product \(a_ k(T)=c\prod_{p}\alpha_ p(T,S),\) where c is a certain constant including the values of the gamma function, \(\alpha_ p(T,S)\) is the so- called p-adic density, and S is a certain matrix. The author gives explicit formulas for \(\alpha_ p(T,S)\) for any odd prime p and non-primitive T. One may note that the explicit formulas for \(\alpha_ p(T,S)\), (i) for odd prime p and primitive T, and (ii) for \(p=2\) and primitive T, have already been given by the reviewer and \textit{T. Washio} [J. Reine Angew. Math. 345, 148-171 (1983; Zbl 0512.10022)]. The case, when \(p=2\) and T is non-primitive, remains open.
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 3877279
zbMATH Keywords: local densities
zbMATH Keywords: explicit formulas
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: Eisenstein series of degree 3
zbMATH Keywords: even weight
reviewed by: Michio Ozeki
MaRDI profile type: Publication
full work available at URL: pjaa.60.259
OpenAlex ID: W2070479933
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DOI: 10.3792/PJAA.60.259
description: scientific article; zbMATH DE number 3877279