On the vanishing of and spanning sets for Poincaré series for cusp forms

DOI10.1007/BF02392375zbMath0543.30037OpenAlexW2004344227MaRDI QIDQ795963

Irwin Kra

Publication date: 1984

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392375

zbMATH Keywords

Poincaré seriesSchottky groupBers spaceBers mapEichler cohomology theory for Kleinian groupsPoincaré vanishing problem

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (13)

On cohomology of finitely generated function groups ⋮ Eichler integrals and string theory ⋮ Poincaré series on bounded symmetric domains ⋮ Deforming super Riemann surfaces with gravitinos and super Schottky groups ⋮ Accessory Parameters for Punctured Spheres ⋮ Families of univalent functions and Kleinian groups ⋮ Approximation by meromorphic \(k\)-differentials on compact Riemann surfaces ⋮ Legendrian tori and the semi-classical limit ⋮ Approximation of a Map Between One-Dimensional Teichmüller Spaces ⋮ On the vanishing of Poincaré series of rational functions ⋮ On cohomology of Kleinian groups. IV: Ahlfors-Sullivan construction of holomorphic Eichler integrals ⋮ On holomorphick-differentials on open Riemann surfaces ⋮ Cusp forms associated to loxodromic elements of Kleinian groups

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