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JACOBI-LIKE FORMS, PSEUDODIFFERENTIAL OPERATORS, AND GROUP COHOMOLOGY

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 August 2008

MIN HO LEE
MIN HO LEE*
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA (email: lee@math.uni.edu)
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Abstract

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Pseudodifferential operators are formal Laurent series in the formal inverse ∂−1 of the derivative operator ∂ whose coefficients are holomorphic functions on the Poincaré upper half-plane. Given a discrete subgroup Γ of SL(2,ℝ), automorphic pseudodifferential operators for Γ are pseudodifferential operators that are Γ-invariant, and they are closely linked to Jacobi-like forms and modular forms for Γ. We construct linear maps from the space of automorphic pseudodifferential operators and from the space of Jacobi-like forms for Γ to the cohomology space of the group Γ, and prove that these maps are compatible with the respective Hecke operator actions.

Keywords

Jacobi-like formspseudodifferential operatorsgroup cohomologyHecke operators

MSC classification

Secondary: 11F50: Jacobi forms 11F11: Holomorphic modular forms of integral weight 11F75: Cohomology of arithmetic groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 55 - 71
Copyright
Copyright © 2008 Australian Mathematical Society

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