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Automorphic forms for subgroups of the modular group

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Abstract

The theory of theta constants with rational characteristics is developed from the point of view of automorphic functions for the principal congruence subgroups of the modular group PSL(2, ℤ). New identities are derived and particular emphasis is given to the level 3 case where a striking generalization of the classical λ-function is obtained.

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References

  1. H. M. Farkas and I. Kra,Riemann Surfaces (second edition), Graduate Texts in Mathematics, Vol. 71, Springer-Verlag, Berlin, 1992.

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  3. I. Kra,Automorphic Forms and Kleinian Groups, Benjamin, New York, 1972.

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  4. H. E. Rauch and H. M. Farkas,Theta Functions with Applications to Riemann Surfaces, Williams and Wilkins, Baltimore, 1974.

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  5. G. Shimura,Introduction to the Arithmetic Theory of Automorphic Functions, Kano memorial lectures, Vol. 1, Iwannami Shoten, Publisher and Princeton University Press, 1971.

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Hershel M. Farkas

  2. Department of Mathematics, State University of New York at Stony Brook, 11794, Stony Brook, NY, USA

    Irwin Kra

Authors
  1. Hershel M. Farkas
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  2. Irwin Kra
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Additional information

This paper is dedicated to Prof. J. Thompson in recognition of his many contributions to mathematics and of his being the recipient of the Wolf Prize in Mathematics

Research by HMF supported in part by the Paul and Gabriella Rosenbaum Foundation and partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany). Research by IK supported in part by NSF Grants DMS 9003361 and 9204092.

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Farkas, H.M., Kra, I. Automorphic forms for subgroups of the modular group. Israel J. Math. 82, 87–131 (1993). https://doi.org/10.1007/BF02808109

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  • DOI: https://doi.org/10.1007/BF02808109

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