manuscripta mathematica

, Volume 107, Issue 4, pp 409–449

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

  • Jens Funke
  • John Millson

DOI: 10.1007/s002290100241

Cite this article as:
Funke, J. & Millson, J. manuscripta math. (2002) 107: 409. doi:10.1007/s002290100241


Using the theta correspondence, we study a lift from (not necessarily rapidly decreasing) closed differential (pn)-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.

Mathematics Subject Classification (2000): 11F27, 11F30, 11F46, 11F75 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jens Funke
    • 1
  • John Millson
    • 2
  1. 1.Department of Mathematics, Rawles Hall, Indiana University, Bloomington,¶IN 47405, USA. e-mail: jefunke@indiana.eduUS
  2. 2.Department of Mathematics, University of Maryland, College Park, MD 20742, USA. e-mail: jjm@math.umd.eduUS

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