The distribution of the zeros of Jacobian elliptic functions with respect to the parameter \(k\) (Q1045731)

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 \(r\).