Jacobi-like forms, pseudodifferential operators, and group cohomology
group cohomology, Hecke operators, Jacobi-like forms, pseudodifferential operators
Bulletin of the Australian Mathematical Society
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
DOI of published version
Lee, Min ho, "Jacobi-like forms, pseudodifferential operators, and group cohomology" (2008). Faculty Publications. 2481.