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.
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.
|Full text:||(AM) Accepted Manuscript|
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|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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