On Siegel series for Hermitian forms
type: Item
instance of: scholarly article
title: On Siegel series for Hermitian forms
zbMATH Open document ID: 0626.10025
author: Shoyu Nagaoka
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: Let K be an imaginary quadratic number field of class number 1. Consider a complex number s with \(Re(s)>4\) and an over K semi-integral positive semi-definite Hermitian \(2\times 2\) matrix H. The author studies the singular series b(s,H), which appears in the Fourier expansion of the Eisenstein series (related with K) on the Hermitian half-space of degree 2. An explicit formula for b(s,H) in terms of Dirichlet series is derived. Then the author generalizes \textit{G. Kaufhold}'s result [Math. Ann. 137, 454-476 (1959; Zbl 0086.067)] and obtains meromorphic continuation and functional equation for the nonanalytic Eisenstein series.
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 4017004
zbMATH Keywords: Siegel series
zbMATH Keywords: Hermitian modular forms
zbMATH Keywords: singular series
zbMATH Keywords: meromorphic continuation
zbMATH Keywords: functional equation
zbMATH Keywords: nonanalytic Eisenstein series
MaRDI profile type: Publication
full work available at URL: pjaa.63.73
OpenAlex ID: W4247047391
cites work: Hermitian modular functions
cites work: Dirichletsche Reihe mit Funktionalgleichung in der Theorie der Modulfunktion 2. Grades
cites work: Dirichlet series in the theory of Siegel modular forms
cites work: Confluent hypergeometric functions on tube domains
cites work: On Eisenstein series
cites work: Einführung in die Theorie der Modulfunktionen \(n\)-ten Grades
DOI: 10.3792/PJAA.63.73
description: scientific article; zbMATH DE number 4017004