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Rational period functions of the modular group II

Published online by Cambridge University Press:  18 May 2009

Marvin I. Knopp
Marvin I. Knopp
Affiliation:
Temple University, Philadelphia
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In the earlier article [7], I began the study of rational period functions for the modular group Γ(l) = SL(2, Z) (regarded as a group of linear fractional transformations) acting on the Riemann sphere. These are rational functions q(z) which occur in functional equations of the form

where k∈Z and F is a function meromorphic in the upper half-plane ℋ, restricted in growth at the parabolic cusp ∞. The growth restriction may be phrased in terms of the Fourier expansion of F(z) at ∞:

with some μ∈Z. If (1.1) and (1.2) hold, then we call F a modular integral of weight 2k and q(z) the period of F.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 2 , July 1981 , pp. 185 - 197
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

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