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Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms

Funke, J.; Millson, J.

Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms Thumbnail


Authors

J. Millson



Abstract

Using the theta correspondence, we study a lift from (not necessarily rapidly decreasing) closed differential (p−n)-forms on a non-compact arithmetic quotient of hyperbolic p-space to Siegel modular forms of degree n. This generalizes earlier work of Kudla and the second named author (in the case of hyperbolic space). We give a cohomological interpretation of the lift and analyze its Fourier expansion in terms of periods over certain cycles. For Riemann surfaces, i.e., the case p= 2, we obtain a complete description using the theory of Eisenstein cohomology.

Citation

Funke, J., & Millson, J. (2002). Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms. manuscripta mathematica, 107(4), 409-449. https://doi.org/10.1007/s002290100241

Journal Article Type Article
Publication Date Apr 1, 2002
Deposit Date May 13, 2014
Publicly Available Date May 14, 2014
Journal manuscripta mathematica
Print ISSN 0025-2611
Electronic ISSN 1432-1785
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 107
Issue 4
Pages 409-449
DOI https://doi.org/10.1007/s002290100241

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