A trace formula for Hecke operators on Fuchsian groups
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Alexandru A. Popa
Abstract
In this paper we give a trace formula for Hecke operators acting on the cohomology of a Fuchsian group of finite covolume Γ with coefficients in a module V. The proof is based on constructing an operator whose trace on V equals the Lefschetz number of the Hecke correspondence on cohomology, generalizing the operator introduced together with Don Zagier for the modular group.
Funding statement: The author was partially supported by the CNCS-UEFISCDI grant PN-III-P4-ID-PCE-2020-2498.
Acknowledgements
I would like to thank Vicenţiu Paşol for helpful discussions while preparing this paper. I would also like the referee for helpful comments improving the exposition.
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Weil representations of twisted loop groups of type A n (2)
- Local Birkhoff decompositions for loop groups and a finiteness result
- Uniform boundedness of oscillatory singular integrals with rational phases
- On the stabilizer of the graph of linear functions over finite fields
- Global solution and blow-up of critical heat equation with nonlocal interaction
- Locally compact groups with all dense subgroups separable
- On the Kawaguchi–Silverman conjecture for birational automorphisms of irregular varieties
- On isometry groups of gradient Ricci solitons
- Extensions of a theorem of P. Hall on indexes of maximal subgroups
- A trace formula for Hecke operators on Fuchsian groups
- Quasi-hereditary algebras with all standard modules being isomorphic to submodules of projective modules
- Computation of endo-fixed closures in free-abelian times free groups
- Non-vanishing of Maass form 𝐿-functions of cubic level at the central point
- Traces of partition Eisenstein series
- Gabor System based on the unitary dual of the Heisenberg group
- Zeros of linear combinations of Dirichlet 𝐿-functions on the critical line
- Paley inequality for the Weyl transform and its applications
Artikel in diesem Heft
- Frontmatter
- Weil representations of twisted loop groups of type A n (2)
- Local Birkhoff decompositions for loop groups and a finiteness result
- Uniform boundedness of oscillatory singular integrals with rational phases
- On the stabilizer of the graph of linear functions over finite fields
- Global solution and blow-up of critical heat equation with nonlocal interaction
- Locally compact groups with all dense subgroups separable
- On the Kawaguchi–Silverman conjecture for birational automorphisms of irregular varieties
- On isometry groups of gradient Ricci solitons
- Extensions of a theorem of P. Hall on indexes of maximal subgroups
- A trace formula for Hecke operators on Fuchsian groups
- Quasi-hereditary algebras with all standard modules being isomorphic to submodules of projective modules
- Computation of endo-fixed closures in free-abelian times free groups
- Non-vanishing of Maass form 𝐿-functions of cubic level at the central point
- Traces of partition Eisenstein series
- Gabor System based on the unitary dual of the Heisenberg group
- Zeros of linear combinations of Dirichlet 𝐿-functions on the critical line
- Paley inequality for the Weyl transform and its applications
