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

Funke, J. and Millson, J. (2002) 'Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular forms.', Manuscripta mathematica., 107 (4). pp. 409-449.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/s002290100241
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s002290100241.
Date accepted:No date available
Date deposited:14 May 2014
Date of first online publication:April 2002
Date first made open access:No date available

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