scientific article

zbMath0495.10016MaRDI QIDQ3958532

John J. Millson, Stephen S. Kudla

Publication date: 1982

Full work available at URL: http://www.numdam.org/item?id=CM_1982__45_2_207_0

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zbMATH Keywords

intersection numberscongruence subgroupautomorphic formslocally symmetric spacesWeil representationharmonic formsgeodesic cyclesdiscrete subgroups of SO(n,1)Poincare duals

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Theta series; Weil representation; theta correspondences (11F27) Hodge theory in global analysis (58A14) Automorphic forms, one variable (11F12) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (23)

The theta correspondence and harmonic forms. I ⋮ Correspondence of modular forms to cycles associated to \(Sp(p,q)\) ⋮ The theta correspondence and harmonic forms. II ⋮ Intersections of higher-weight cycles over quaternionic modular surfaces and modular forms of Nebentypus ⋮ Unnamed Item ⋮ Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables ⋮ Harmonic differentials and closed geodesics on a Riemann surface ⋮ Theta series and generalized special cycles on Hermitian locally symmetric manifolds ⋮ Holomorphic Siegel modular forms associated to \(SO(n,1)\) ⋮ Harmonic forms dual to geodesic cycles in quotients of SU(p,1) ⋮ Geometric cycles, arithmetic groups and their cohomology ⋮ Theta correspondence for Eisenstein series ⋮ Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups ⋮ Discrete spectrum of the reductive dual pair \((\mathrm{O}(p,q),\mathrm{Sp}(2m))\) ⋮ Unnamed Item ⋮ Harmonic differentials and infinite geodesic joining two punctures on a Riemann surface ⋮ Unnamed Item ⋮ Modularity of generating series of winding numbers ⋮ Theta functions defined by geodesic cycles in quotients of SU(p,1) ⋮ Construction of Cohomology of Discrete Groups ⋮ Hyperbolic Eisenstein series on \(n\)-dimensional hyperbolic spaces ⋮ Dual harmonic form to a quasi-Fuchsian cycle ⋮ Period integrals in noncompact quotients of SU(p,1)

Cites Work

• Geometric construction of cohomology for arithmetic groups. I
• Harmonic differentials and closed geodesics on a Riemann surface
• The Weil representation, Maslov index and theta series
• Modular forms associated to real quadratic fields
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• On modular forms associated with indefinite quadratic forms of signature \((2,n-2)\)
• Über Poincaresche Reihen vom Exponentialtyp
• Intersection numbers for quotients of the complex 2-ball and Hilbert modular forms
• Sur certains groupes d'opérateurs unitaires
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• Siegel's modular forms and Dirichlet series. Course given at the University of Maryland, 1969-1970
• Asymptotic distributions associated with the Laplacian for forms
• Modular forms of half integral weight and the integral of certain theta-functions
• On construction of holomorphic cusp forms of half integral weight
• On the Doi-Naganuma lifting associated with imaginary quadratic fields
• The Structure of Semisimple Symmetric Spaces
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