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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the genus of meromorphic functions
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by Vicente Muñoz and Ricardo Pérez Marco PDF
Proc. Amer. Math. Soc. 143 (2015), 341-351 Request permission

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
  • 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