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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 doubly periodic phases
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by Marius B. Stefan PDF
Proc. Amer. Math. Soc. 142 (2014), 3149-3152 Request permission

Abstract:

Every meromorphic function on $\mathbb {C}$ with doubly periodic phase is equal to an elliptic function multiplied by a meromorphic function determined by the periods.
References
  • N. H. Abel, Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes, Présenté à l’Académie des sciences à Paris le 30 Octobre 1826. Mémoires présentés par divers savants t. VII, Paris (1841).
  • N. H. Abel, Remarques sur quelques propriétés générales d’une certaine sorte de fonctions transcendantes, Oeuvres Complètes, t. I, Christiania (1839), 288-298.
  • N. H. Abel, Démonstration d’une propriété générale d’une certaine classe de fonctions transcendantes, Oeuvres Complètes, t. I, Christiania (1839), 324-325.
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  • K. Weierstrass, Zur Theorie der eindeutigen analytischen Functionen, Mathematische Abhandlungen der Akademie der Wissenschaften zu Berlin (1876), 11-60.
  • K. Weierstrass, Zur Theorie der elliptischen Functionen, Sitzungsberichte der Akademie der Wissenschaften zu Berlin (1882), 443-451.
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Additional Information
  • Marius B. Stefan
  • Affiliation: Waltham, Massachusetts 02453
  • Email: stefanmb@member.ams.org
  • Received by editor(s): November 22, 2011
  • Received by editor(s) in revised form: March 21, 2012, and October 1, 2012
  • Published electronically: May 28, 2014
  • Communicated by: Mario Bonk
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 3149-3152
  • MSC (2010): Primary 30Dxx
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12047-8
  • MathSciNet review: 3223371