On the genus of meromorphic functions

Vicente Muñoz; Ricardo Pérez Marco

On the genus of meromorphic functions

Complex Variables 2013-06-11 v1

Authors: Vicente Muñoz , Ricardo Pérez Marco

Abstract

We define the class of Left Located Divisor (LLD) meromorphic functions and their vertical order $m_0(f)$ and their convergence exponent $d(f)$ . When $m_0(f)\leq d(f)$ we prove that their Weierstrass genus is minimal. This explains the phenomena that many classical functions have minimal Weierstrass genus, for example Dirichlet series, the $\Gamma$ -function, and trigonometric functions.

Keywords

special functions univalent functions

Cite

@article{arxiv.1306.2165,
  title  = {On the genus of meromorphic functions},
  author = {Vicente Muñoz and Ricardo Pérez Marco},
  journal= {arXiv preprint arXiv:1306.2165},
  year   = {2013}
}

Comments

14 pages

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