Eichler cohomology of generalized modular forms of real weights

@article{Raji2012EichlerCO,
  title={Eichler cohomology of generalized modular forms of real weights},
  author={Wissam Raji},
  journal={Scopus},
  year={2012},
  volume={141},
  pages={383-392}
}
  • W. Raji
  • Published 1 May 2012
  • Mathematics
  • Scopus
Bol G., 1949, ABH MATH SEM HAMBURG, V16, P1; Eichler M., 1965, ACTA ARITH, V11, P169; HUSSEINI SY, 1971, ILLINOIS J MATH, V15, P565; Knopp M, 2010, INT J NUMBER THEORY, V6, P1083, DOI 10.1142-S179304211000340X; Knopp M, 2003, J NUMBER THEORY, V99, P1, DOI 10.1016-S0022-314X(02)00065-3; Knopp M, 2009, INT J NUMBER THEORY, V5, P845, DOI 10.1142-S1793042109002419; Knopp M, 2009, INT J NUMBER THEORY, V5, P1049, DOI 10.1142-S1793042109002547; KNOPP MI, 1974, B AM MATH SOC, V80, P607, DOI 10.1090… 
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Eichler cohomology for generalized modular forms ii
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The focus is shifted from generalized modular forms of integral weight to those of arbitrary real weight, and Stokes’s theorem is rendered unnecessary here by its use instead of the appropriate known cohomology theorem with unitary multiplier systems.
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Corrigendum to “Eichler cohomology for generalized modular forms of real weights”

References

SHOWING 1-10 OF 16 REFERENCES
Eichler cohomology for generalized modular forms ii
TLDR
The focus is shifted from generalized modular forms of integral weight to those of arbitrary real weight, and Stokes’s theorem is rendered unnecessary here by its use instead of the appropriate known cohomology theorem with unitary multiplier systems.
Generalized modular forms
PARABOLIC GENERALIZED MODULAR FORMS AND THEIR CHARACTERS
We make a detailed study of the generalized modular forms of weight zero and their associated multiplier systems (characters) on an arbitrary subgroup Γ of finite index in the modular group. Among…
EICHLER COHOMOLOGY THEOREM FOR GENERALIZED MODULAR FORMS
We show starting with relations between Fourier coefficients of weakly parabolic generalized modular forms of negative weight that we can construct automorphic integrals for large integer weights. We…
Construction of automorphic forms and integrals
It is well known that modular forms of positive dimension have Fourier coefficients given by certain infinite series involving Kloostermann sums and the modified Bessel function of the first kind. In…
Fourier coefficients of generalized modular forms of negative weight
The Fourier coefficients of classical modular forms of negative weights have been determined for the case for which F(τ) belongs to a subgroup of the full modular group [9]. In this paper, we…
EICHLER COHOMOLOGY FOR GENERALIZED MODULAR FORMS
By using Stokes's theorem, we prove an Eichler cohomology theorem for generalized modular forms with some restrictions on the relevant multiplier systems.
Konstruktion der Modulformen und der zu gewissen Grenzkreisgruppen gehörigen automorphen Formen von positiver reeller Dimension und die vollständige Bestimmung ihrer Fourierkoeffizienten
Das Problem, die Fourier-Koeffizienten der Modulformen von positiver Dimension zu bestimmen, das hier fur die Funktionen der vollen Modulgruppe und fur die gewisser Grenzkreisgruppen von beliebigem…
Construction of generalized modular integrals
In this paper, we find a functional equation that characterizes the series involved in the Fourier coefficients of generalized modular forms of large negative real weights.
Some new results on the Eichler cohomology of automorphic forms
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