Kocher-Maaß-series for modular forms of quaternions
type: Item
instance of: scholarly article
title: Kocher-Maaß-series for modular forms of quaternions
zbMATH Open document ID: 0698.10019
DOI: 10.1007/BF02568507
author: Aloys Krieg
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155483
review text: In previous work [``Modular Forms on Half-Spaces of Quaternions'', Lect. Notes Math. 1143 (1985; Zbl 0564.10032)] the author created a theory of modular forms of quaternions following closely the classical lines of the theory of Siegel modular forms. As in the Siegel case one can attach to a modular form of quaternions a Dirichlet series by a generalized Mellin transform. In the paper under review the author proves meromorphic continuation and functional equation of such Dirichlet series along the lines of \textit{H. Maa}'s work [``Siegel's Modular Forms and Dirichlet Series'', Lect. Notes Math. 216 (1971; Zbl 0224.10028)] on the Siegel case. To determine poles and residues the author uses a method of \textit{T. Arakawa} [Math. Ann. 238, 157-173 (1978; Zbl 0373.10017)]. Surprisingly (and in contrast to the Siegel case) this Dirichlet series has an Euler product expansion, if the modular form in question is a Hecke eigenform in the Maa space.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 4144057
zbMATH Keywords: modular forms of quaternions
zbMATH Keywords: Dirichlet series
zbMATH Keywords: meromorphic continuation
zbMATH Keywords: functional equation
zbMATH Keywords: poles
zbMATH Keywords: residues
zbMATH Keywords: Euler product expansion
zbMATH Keywords: Hecke eigenform
zbMATH Keywords: Maa space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4144057