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The Distribution of the Zeros of Jacobian Elliptic Functions with Respect to the Parameter k

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Abstract

We investigate the distribution of the zeros of the twelve Jacobian elliptic functions sn(z, k), etc. as functions of k for fixed z. We show that the number of zeros inside a disc given by ¦k¦ ≤ r is approximately of order r 2 and hence that the mapping k ↦ sn(z, k) is of order 2.

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  1. 7 Redgrove Park, Cheltenham, GL51 6QY, UK

    Peter L. Walker

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  1. Peter L. Walker
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Correspondence to Peter L. Walker.

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Walker, P.L. The Distribution of the Zeros of Jacobian Elliptic Functions with Respect to the Parameter k . Comput. Methods Funct. Theory 9, 579–591 (2009). https://doi.org/10.1007/BF03321746

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  • DOI: https://doi.org/10.1007/BF03321746

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