Computational Methods and Function Theory 9 (2009), No. 2, 579--591
Copyright Heldermann Verlag 2009
Peter L. Walker
peter.walker@cantab.net , 7 Redgrove Park, Cheltenham, GL51 6QY, U.K.
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 r2 and hence that the mapping k→sn(z,k) is of order 2.
Keywords: Elliptic functions, Jacobian functions, distribution of zeros.
MSC 2000: 30D15, 33E05.
[FullText-pdf (268 K)] [FullText-ps (856 K)]