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On the genus of meromorphic functions

Authors: Vicente Muñoz and Ricardo Pérez Marco
Journal: Proc. Amer. Math. Soc. 143 (2015), 341-351
MSC (2010): Primary 30D30; Secondary 30B50, 30D15
Published electronically: September 15, 2014
MathSciNet review: 3272759
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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.

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Additional Information

Vicente Muñoz
Affiliation: Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain

Ricardo Pérez Marco
Affiliation: CNRS, LAGA UMR 7539, Université Paris XIII, 99, Avenue J.-B. Clément, 93430-Villetaneuse, France

Keywords: Dirichlet series, Poisson-Newton formula, Hadamard factorization.
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
Article copyright: © Copyright 2014 American Mathematical Society

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