Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T04:57:52.772Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixed cusp forms and parabolic cohomology

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  09 April 2009

Min Ho Lee
Min Ho Lee
Affiliation:
Department of Mathematics University of Northern Iowa, Cedar Falls Iowa 50614, USA, e-mail: lee@math.uni.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Sk, l(Γ, ω, χ) be the space of mixed cusp forms of type (k, l) associated to a Fuchsian group Γ, a holomorphic map ω: ℋ → ℋ of the upper half plane into itself and a homomorphism χ: Γ → SL(2, R) such that ω and χ are equivariant. We construct a map from Sk, l(Γ, ω, χ) to the parabolic cohomology space of Γ with coefficients in some Γ-module and prove that this map is injective.

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight 11F30: Fourier coefficients of automorphic forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 279 - 289
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Cox, D. and Zucker, S., ‘Intersection numbers of sections of elliptic surfaces’, Invent. Math. 53 (1979), 1–44.Google Scholar
[2]Eichler, M., ‘Eine Verallgemeinerung der Abelschen Integrale’, Math. Z. 67 (1957), 267–298.Google Scholar
[3]Hida, H., Elementary theory of L-functions and Eisenstein series (Cambridge Univ. Press, Cambridge, 1993).Google Scholar
[4]Hunt, B. and Meyer, W., ‘Mixed automorphic forms and invariants of elliptic surfaces’, Math. Ann. 271 (1985), 53–80.Google Scholar
[5]Lee, M. H., ‘Mixed cusp forms and holomorphic forms on elliptic varieties’, Pacific J. Math. 132 (1988), 363–370.Google Scholar
[6]Lee, M. H., ‘Periods of mixed cusp forms’, Manuscripta Math. 73 (1991), 163–177.Google Scholar
[7]Lee, M. H., ‘Mixed cusp forms and Poincaré series’, Rocky Mountain J. Math. 23 (1993), 1009–1022.Google Scholar
[8]Lee, M. H., ‘Mixed Siegel modular forms and Kuga fiber varieties’, Illinois J. Math. 38 (1994), 692–700.Google Scholar
[9]Lee, M. H., ‘Mixed automorphic vector bundles on Shimura varieties’, Pacific J. Math. 173 (1996), 105–226.CrossRefGoogle Scholar
[10]Shimura, G., ‘Sur les intégrales attachés aux formes automorphes’, J. Math. Soc. Japan 11 (1959), 291–311.Google Scholar
[11]Shimura, G., Arithmetic theory of automorphic functions (Princeton Univ. Press, Princeton, 1971).Google Scholar