zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
The distribution of the zeros of Jacobian elliptic functions with respect to the parameter $k$. (English) Zbl 1183.30023
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 $z\in ℂ$, we denote by $n\left(r\right)$ the number of zeros of the function $m↦\text{sn}\left(z|m\right)$ (or any other Jacobian function) inside the disc $|m|\le r$, then $Ar{\left(logr\right)}^{-2}\le n\left(r\right)\le Br$ for some constants $A$ and $B$ and for sufficiently large $r$.
MSC:
 30D15 Special classes of entire functions; growth estimates 33E05 Elliptic functions and integrals
References:
 [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, volume AMS 55, NBS, U. S. Government Printing Office, Washington, DC, USA, 1964. [2] A. F. Beardon, Complex Analysis, Wiley, Chichester, UK, 1979. [3] K. Chandrasekharan, Elliptic Functions, volume 281 of Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, Germany, 1985. [4] H. E. Fettis, On the reciprocal modulus relation for elliptic integrals, SIAM J. Math. Anal. 1 (1970), 524–526. · Zbl 0202.34202 · doi:10.1137/0501045 [5] P. L. Walker, The analyticity of Jacobian functions with respect to the parameter k, Proc. R. Soc. Lond. A 8 (2003), 2569–2574. · Zbl 1052.33018 · doi:10.1098/rspa.2003.1157