Weil representations associated with finite quadratic modules

DOI10.1007/s00209-013-1145-xzbMath1327.11032arXiv1108.0202OpenAlexW1985900554MaRDI QIDQ379223

Fredrik Strömberg

Publication date: 11 November 2013

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.0202

zbMATH Keywords

Weil representationmetaplectic groupfinite quadratic module

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27)

Related Items (28)

Poincaré square series for the Weil representation ⋮ ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS ⋮ Vector valued theta functions associated with binary quadratic forms ⋮ Generating weights for the Weil representation attached to an even order cyclic quadratic module ⋮ Theta series for quadratic forms of signature (n − 1,1) with (spherical) polynomials ⋮ On the restriction map for Jacobi forms ⋮ Relations among Ramanujan-type congruences II: Ramanujan-type congruences in half-integral weights ⋮ Unnamed Item ⋮ On pullbacks of functions of lattice-index and an infinite family of Siegel cusp forms ⋮ Integral bases and invariant vectors for Weil representations ⋮ Shintani lifts of nearly holomorphic modular forms ⋮ A Gross-Kohnen-Zagier type theorem for higher-codimensional Heegner cycles ⋮ Seesaw identities and theta contractions with generalized theta functions, and restrictions of theta lifts ⋮ Quasi‐pullback of Borcherds products ⋮ On liftings of modular forms and Weil representations ⋮ Taylor expansions of Jacobi forms and linear relations among theta series ⋮ Finite quadratic modules and lattices ⋮ Double coset operators and eta-quotients ⋮ A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS ⋮ Shimura lifts of weakly holomorphic modular forms ⋮ Jacobi forms of indefinite lattice index ⋮ The Fourier expansion of Hecke operators for vector-valued modular forms ⋮ Half-integral weight modular forms and modular forms for Weil representations ⋮ Lattices with many Borcherds products ⋮ On explicit isomorphisms of spaces of Jacobi forms of lattice-index ⋮ Rationality and \(p\)-adic properties of reduced forms of half-integral weight ⋮ Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two ⋮ On two arithmetic theta lifts

Uses Software

• SageMath

Cites Work

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• Lectures on modular functions of one complex variable. Notes by Sunder Lal. Rev. ed
• Weil's representation and the spectrum of the metaplectic group
• Reflection groups of Lorentzian lattices
• Topological covering of SL(2) over a local field
• Sur certains groupes d'opérateurs unitaires
• On modular forms of half integral weight
• Die Wirkung der Modulsubstitutionen auf mehrfache Thetareihen zu quadratischen Formen ungerader Variablenzahl
• The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups. I, II
• Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two
• Computation of Harmonic Weak Maass Forms
• The Weil Representation of and Some Applications
• On construction of holomorphic cusp forms of half integral weight

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