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On Saito-Kurokawa descent for congruence subgroups

On Saito-Kurokawa descent for congruence subgroups The conjecture made by H. Saito and N. Kurokawa states the existence of a “lifting” from the space of elliptic modular forms of weight 2k−2 (for the full modular group) to the subspace of the space of Siegel modular forms of weightk (for the full Siegel modular group) which is compatible with the action of Hecke operators. (The subspace is the so called “Maaß spezialschar” defined by certain identities among Fourier coefficients). This conjecture was proved (in parts) by H. Maaß, A.N. Andrianov and D. Zagier. The purpose of this paper is to prove a generalised version of the conjecture for cusp forms of odd squarefree level. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Manuscripta Mathematica Springer Journals

On Saito-Kurokawa descent for congruence subgroups

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 1993 by Springer-Verlag
Subject
Mathematics; Mathematics, general; Algebraic Geometry; Topological Groups, Lie Groups; Geometry; Number Theory; Calculus of Variations and Optimal Control; Optimization
ISSN
0025-2611
eISSN
1432-1785
DOI
10.1007/BF02567852
Publisher site
See Article on Publisher Site

Abstract

The conjecture made by H. Saito and N. Kurokawa states the existence of a “lifting” from the space of elliptic modular forms of weight 2k−2 (for the full modular group) to the subspace of the space of Siegel modular forms of weightk (for the full Siegel modular group) which is compatible with the action of Hecke operators. (The subspace is the so called “Maaß spezialschar” defined by certain identities among Fourier coefficients). This conjecture was proved (in parts) by H. Maaß, A.N. Andrianov and D. Zagier. The purpose of this paper is to prove a generalised version of the conjecture for cusp forms of odd squarefree level.

Journal

Manuscripta MathematicaSpringer Journals

Published: Dec 1, 1993

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