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Equivariant functions and integrals of elliptic functions

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In this paper, we introduce the theory of equivariant functions by studying their analytic, geometric and algebraic properties. We also determine the necessary and sufficient conditions under which an equivariant form arises from modular forms. This study was motivated by observing examples of functions for which the Schwarzian derivative is a modular form on a discrete group. We also investigate the Fourier expansions of normalized equivariant functions, and a strong emphasis is made on the connections to elliptic functions and their integrals.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada

    Abdellah Sebbar

  2. Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 33405, Talence cedex, France

    Ahmed Sebbar

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  1. Abdellah Sebbar
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  2. Ahmed Sebbar
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Correspondence to Ahmed Sebbar.

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Sebbar, A., Sebbar, A. Equivariant functions and integrals of elliptic functions. Geom Dedicata 160, 373–414 (2012). https://doi.org/10.1007/s10711-011-9688-7

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  • DOI: https://doi.org/10.1007/s10711-011-9688-7

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