Faculty Publications

Title

Jacobi-like forms, pseudodifferential operators, and group cohomology

Document Type

Article

Keywords

group cohomology, Hecke operators, Jacobi-like forms, pseudodifferential operators

Journal/Book/Conference Title

Bulletin of the Australian Mathematical Society

Volume

78

Issue

1

First Page

55

Last Page

71

Abstract

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,[formula omitted]), 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. © 2008, Australian Mathematical Society. All rights reserved.

Original Publication Date

1-1-2008

DOI of published version

10.1017/S0004972708000476

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