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Zbl 1183.30023
Walker, Peter L.
The distribution of the zeros of Jacobian elliptic functions with respect to the parameter $k$. (English)
[J] Comput. Methods Funct. Theory 9, No. 2, 579-591 (2009). ISSN 1617-9447; ISSN 2195-3724/e

In the paper under review, the author studies the size of the complete elliptic integral and the conjugate elliptic integral. Then after, he shows that if for given $z\in\mathbb{C}$, we denote by $n(r)$ the number of zeros of the function $m\mapsto\text{sn}(z|m)$ (or any other Jacobian function) inside the disc $|m|\leq r$, then $Ar(\log r)^{-2}\leq n(r)\leq Br$ for some constants $A$ and $B$ and for sufficiently large $r$.
[Mehdi Hassani (Zanjan)]

MSC 2000:: *30D15 Special classes of entire functions
33E05 Elliptic functions and integrals

Keywords: elliptic functions; Jacobian functions; distribution of zeros

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