The theta correspondence and harmonic forms. II

DOI10.1007/BF01457364zbMath0618.10022MaRDI QIDQ1089031

Stephen S. Kudla, John J. Millson

Publication date: 1987

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

Full work available at URL: https://eudml.org/doc/164250

zbMATH Keywords

symmetric spacesautomorphic formsSchwartz spacecontinuous cohomologytheta-correspondencedual reductive pairautomorphic classescohomology classes of arithmetic quotientsgenerating function for intersection numbersGeodesic cycles

Mathematics Subject Classification ID

Homology and cohomology of Lie groups (57T10) Discrete subgroups of Lie groups (22E40) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Automorphic forms, one variable (11F12)

Related Items (37)

The theta correspondence and harmonic forms. I ⋮ Indefinite theta series and generalized error functions ⋮ Moduli spaces and modular forms. Abstracts from the workshop held January 31 -- February 6, 2021 (hybrid meeting) ⋮ On the subring of special cycles ⋮ Ternary quadratic forms and Heegner divisors ⋮ Relative trace formulas for unitary hyperbolic spaces ⋮ Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables ⋮ On class number relations and intersections over function fields ⋮ Mock modular forms and geometric theta functions for indefinite quadratic forms ⋮ On CM masses over global function fields ⋮ Diagonal restriction of Eisenstein series and Kudla-Millson theta lift ⋮ Theta series and generalized special cycles on Hermitian locally symmetric manifolds ⋮ On recursive properties of certain \(p\)-adic Whittaker functions ⋮ Siegel theta series for quadratic forms of signature \((m - 1, 1)\) ⋮ Theta integrals and generalized error functions ⋮ The geometric theta correspondence for Hilbert modular surfaces ⋮ Generating series of a new class of orthogonal Shimura varieties ⋮ Superconnections, theta series, and period domains ⋮ Algebraic cycles on Shimura varieties of orthogonal type ⋮ Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups ⋮ The Hodge conjecture and arithmetic quotients of complex balls ⋮ On two geometric theta lifts ⋮ Hilbert Modular Forms and Their Applications ⋮ Formal Fourier Jacobi expansions and special cycles of codimension two ⋮ Unnamed Item ⋮ Arithmetic degrees of special cycles and derivatives of Siegel Eisenstein series ⋮ Siegel theta series for indefinite quadratic forms ⋮ Black holes and higher depth mock modular forms ⋮ Certain Rankin-Selberg integral for unitary groups ⋮ On some incomplete theta integrals ⋮ Modularity of generating series of winding numbers ⋮ Remarks on generating series for special cycles on orthogonal Shimura varieties ⋮ Boundary behaviour of special cohomology classes arising from the Weil representation ⋮ The construction of Green currents and singular theta lifts for unitary groups ⋮ Weak Siegel-Weil formula for 𝕄₂(ℚ) and arithmetic on quaternions ⋮ Some cases of Kudla’s modularity conjecture for unitary Shimura varieties ⋮ Regularized theta lifts for orthogonal groups over totally real fields

Cites Work

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• Period integrals in noncompact quotients of SU(p,1)
• The theta correspondence and harmonic forms. I
• Correspondence of modular forms to cycles associated to O(p,q)
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• Discrete series for semisimple symmetric spaces
• Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
• Theta functions defined by geodesic cycles in quotients of SU(p,1)
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• Arithmetic cycles on Picard modular surfaces and modular forms of Nebentypus.
• Cycles and Harmonic Forms on Locally Symmetric Spaces
• Tubes, Cohomology with Growth Conditions and an Application to the Theta Correspondence
• On construction of holomorphic cusp forms of half integral weight

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