On the genus of meromorphic functions
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- by Vicente Muñoz and Ricardo Pérez Marco
- Proc. Amer. Math. Soc. 143 (2015), 341-351
- DOI: https://doi.org/10.1090/S0002-9939-2014-12370-7
- Published electronically: September 15, 2014
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Abstract:
We define the class of Left Located Divisor (LLD) meromorphic functions, 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.References
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Bibliographic Information
- Vicente Muñoz
- Affiliation: Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
- Email: vicente.munoz@mat.ucm.es
- Ricardo Pérez Marco
- Affiliation: CNRS, LAGA UMR 7539, Université Paris XIII, 99, Avenue J.-B. Clément, 93430-Villetaneuse, France
- MR Author ID: 308175
- Email: ricardo@math.univ-paris13.fr
- Received by editor(s): April 30, 2013
- Published electronically: September 15, 2014
- Additional Notes: The authors were partially supported through Spanish MICINN grant MTM2010-17389.
- Communicated by: Franc Forstneric
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 341-351
- MSC (2010): Primary 30D30; Secondary 30B50, 30D15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12370-7
- MathSciNet review: 3272759