Petersson norms and liftings of Hilbert modular forms
type: Item
instance of: scholarly article
title: Petersson norms and liftings of Hilbert modular forms
zbMATH Open document ID: 1050.11051
author: Dominic Lanphier
published in: Journal of Number Theory
publication date: 2004-08-04T00:00:00Z
review text: Vergleiche der Norm einer Modulform mit der Norm ihrer Liftung zu einer Hilbertschen Modul\-form (Saito-Kurokawa-Liftung) durch \textit{M. Furusawa} [Math. Ann. 267, 543--548 (1984; Zbl 0519.10020)] und \textit{W. Kohnen} [J. Reine Angew. Math. 357, 96--100 (1985; Zbl 0547.10026)] zeigten, dass sich diese Normen bis auf triviale Faktoren nur um einen algebraischen Zahlenfaktor aus einem ganz bestimmten Körper unterscheiden. In Verallgemeinerungen, etwa bei \textit{G. Shimura} [Arithmeticity in the theory of automorphic forms (Mathematical Surveys and Monographs 82, AMS, Providence RI) (2000; Zbl 0967.11001)] trat dann an Stelle der Norm der Liftung ein spezieller Wert einer \(L\)-Reihe auf. Verf. erweitert die Resultate der Arbeiten von Furusawa und beweist insbesondere eine Verallgemeinerung des Satzes 28.8 des erwähnten Buches von Shimura über den Zahlenfaktor, indem er das Verhalten unter Galoistransformationen ermittelt.
reviewed by: Karl-Bernhard Gundlach
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 2081160
zbMATH Keywords: Hilbert modular form
zbMATH Keywords: Eisenstein series
zbMATH Keywords: \(L\)-function
zbMATH Keywords: Saito-Kurokawa lift
zbMATH Keywords: Ikeda lift
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.01.003
OpenAlex ID: W1980958943
cites work: Q5629705
cites work: Siegel modular forms and representations
cites work: Über Funktionalgleichungen automorpher L-Funktionen zur Siegelschen Modulgruppe.
cites work: On the Petersson norm of certain Siegel modular forms
cites work: Base change for the Saito-Kurokawa representations of PGSp(4)
cites work: The theory of Jacobi forms
cites work: On Petersson norms for some liftings
cites work: Q3824482
cites work: Q3993071
cites work: On the arithmetic of Siegel-Hilbert cusp forms: Petersson inner products and Fourier coefficients
cites work: Explicit constructions of automorphic \(L\)-functions
cites work: Eisenstein series on Shimura varieties
cites work: On the lifting of elliptic cusp forms to Siegel cusp forms of degree \(2n\)
cites work: Q3741813
cites work: On the Petersson norm of a Siegel-Hecke Eigenform of degree two in the Maass space.
cites work: On the Linear Representability of Siegel-Hilbert Modular Forms by Theta Series
cites work: On Saito-Kurokawa descent for congruence subgroups
cites work: On the Saito-Kurokawa lifting
cites work: Q3325945
cites work: The special values of the zeta functions associated with Hilbert modular forms
cites work: Q3901580
DOI: 10.1016/J.JNT.2004.01.003
Recommended article: On the Petersson norm of certain Siegel modular forms
Recommended article: The lifting of elliptic modular forms to Hilbert modular forms and Petersson inner products
Recommended article: Petersson norms of not necessarily cuspidal Jacobi modular forms and applications
Recommended article: Petersson's trace formula and the Hecke eigenvalues of Hilbert modular forms
Recommended article: On the Petersson norm of the Hilbert-Siegel cusp form under the Ikeda lift
Recommended article: On Shimura lifting of Hilbert modular forms
Recommended article: Q3139678
Recommended article: RELÈVEMENT DES FORMES MODULAIRES DE PICARD
Recommended article: Petersson scalar products and \(L\)-functions arising from modular forms
Recommended article: On Liftings of Holomorphic Modular Forms
description: scientific article; zbMATH DE number 2081160