Period Functions for Maass Wave Forms and Cohomology

DOI10.1090/memo/1118zbMath1396.11072OpenAlexW2049909177MaRDI QIDQ2944989

Don Zagier, Roelof Wichert Bruggeman, John B. Lewis

Publication date: 9 September 2015

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://dspace.library.uu.nl/handle/1874/377849

zbMATH Keywords

cup productcohomology groupprincipal seriesMaass formperiod functionPetersson scalar productparabolic cohomology

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Discrete subgroups of Lie groups (22E40) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Cohomology of arithmetic groups (11F75)

Related Items (17)

Ruelle-Pollicott resonances for manifolds with hyperbolic cusps ⋮ Eigenfunctions of transfer operators and cohomology ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ Eigenfunctions of Transfer Operators and Automorphic Forms for Hecke Triangle Groups of Infinite Covolume ⋮ Even Galois representations and the cohomology of \(\text{GL}(2,\mathbb Z)\) ⋮ Higher rank quantum-classical correspondence ⋮ Dynamics of a family of continued fraction maps ⋮ The Eichler-Shimura cohomology theorem for Jacobi forms ⋮ Modular cocycles and cup product ⋮ Periods of Jacobi forms and the Hecke operator ⋮ A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area ⋮ Series expansions for Maass forms on the full modular group from the Farey transfer operators ⋮ Parabolic cohomology and multiple Hecke \(L\)-values ⋮ A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions ⋮ Dynamics of geodesics, and Maass cusp forms ⋮ Holomorphic modular forms and cocycles ⋮ Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

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