On classical Saito-Kurokawa liftings

DOI10.1515/CRELLE.2007.024zbMath1118.11027OpenAlexW2095527879MaRDI QIDQ3445254

Ralf Schmidt

Publication date: 8 June 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2007.024

zbMATH Keywords

Siegel modular formautomorphic representationSaito-Kurokawa liftelliptic modular formspin \(L\)-function

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Hecke-Petersson operators, differential operators (one variable) (11F25) Modular correspondences, etc. (11F32)

Related Items (max. 100)

On counting cuspidal automorphic representations for \(\mathrm{GSp(4)}\) ⋮ Maass relations for Saito-Kurokawa lifts of higher levels ⋮ Klingen \(\mathfrak{p}^2\) vectors for \(\text{GSp}(4)\) ⋮ Fourier coefficients for twists of Siegel paramodular forms (expanded version) ⋮ Lifting congruences to half-integral weight ⋮ Congruences of Siegel Eisenstein series of degree two ⋮ Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level ⋮ Local and global Maass relations ⋮ On Siegel eigenvarieties at Saito-Kurokawa points ⋮ Congruences modulo 2 for dimensions of spaces of cusp forms ⋮ Level stripping for Siegel modular forms with reducible Galois representations ⋮ Equidistribution theorems for holomorphic Siegel modular forms for \(\mathrm{GSp}_4\); Hecke fields and \(n\)-level density ⋮ Survey article: Characterizations of the Saito-Kurokawa lifting ⋮ Hermitian Maass lift for general level ⋮ On the Bloch-Kato conjecture for elliptic modular forms of square-free level ⋮ Paramodular forms in CAP representations of ${\rm GSp}(4)$ ⋮ Formulas for central values of twisted spin $L$-functions attached to paramodular forms ⋮ Irreducibility of limits of Galois representations of Saito-Kurokawa type ⋮ Mixed-level Saito-Kurokawa liftings ⋮ Multiplicity formulas for discrete series representations in \(L^2(\Gamma\setminus\mathrm{Sp}(2,\mathbb R))\) ⋮ Conjectures on correspondence of symplectic modular forms of middle parahoric type and Ihara lifts ⋮ CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE ⋮ Paramodular forms of level 8 and weights 10 and 12

Cites Work

• Modular descent and the Saito-Kurokawa conjecture
• On the Saito-Kurokawa lifting
• Proof of the Deligne-Langlands conjecture for Hecke algebras
• Jacobi forms and a certain space of modular forms
• Siegel's modular forms and the arithmetic of quadratic forms
• Über eine Spezialschar von Modulformen zweiten Grades. (On a Spezialschar of modular forms of second degree.)
• Examples of eigenvalues of Hecke operators on Siegel cusp forms of degree two
• On Saito-Kurokawa descent for congruence subgroups
• Iwahori-spherical representations of \(\mathrm{GSp}(4)\) and Siegel modular forms of degree 2 with square-free level
• On Saito-Kurokawa lifting to cohomological Siegel modular forms
• The Saito-Kurokawa lifting and functoriality
• On Shimura, Shintani and Eichler-Zagier correspondences
• Correspondances de Shimura et quaternions
• Siegel modular forms and representations
• Quadratic base change of \(\theta_{10}\)

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