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Pólya's Shire Theorem for Automorphic Functions

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Abstract

Generalizing a classic result by Pólya concerning the zeros of successive derivatives of meromorphic functions in the complex plane, we study the accumulation set of zeros of successive derivatives of automorphic functions in the hyperbolic plane, as well as the connection between the automorphism group and the topology of this set in the Poincaré disk model.

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Authors and Affiliations

  1. Case Western Reserve University, Cleveland, OH, 44106, U.S.A.

    Matthias Weiss

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  1. Matthias Weiss
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Weiss, M. Pólya's Shire Theorem for Automorphic Functions. Geometriae Dedicata 100, 85–92 (2003). https://doi.org/10.1023/A:1025855513977

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