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The Schneider-Lang theorem for functions with essential singularities

Author: Jack Diamond
Journal: Proc. Amer. Math. Soc. 80 (1980), 223-226
MSC: Primary 10F35; Secondary 10F45
MathSciNet review: 577748
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Abstract: A new proof of Schwarz's lemma for functions with a finite number of essential singularities is given. The proof is valid for p-adic as well as complex functions and is used to extend Bertrand's version of the Schneider-Lang theorem for p-adic functions with one, common, finite singularity to functions with finitely many singularities.

References [Enhancements On Off] (What's this?)

  • [1] D. Bertrand, Un théorème de Schneider-Lang sur certains domaines non simplement connexes, Séminaire Delange-Pisot-Poitou (16e année: 1974/75), Théorie des Nombres, Fasc. 2, Exp. No. G-18, Secrétariat Mathématique, Paris, 1975. MR 0401661 (53:5488)
  • [2] -, Séries d'Eisenstein et transcendance, Bull. Soc. Math. France, 104 (1976), 309-321. MR 0437468 (55:10398)
  • [3] S. Lang, Introduction to transcendental numbers, Addison-Wesley, Reading, Mass., 1966. MR 0214547 (35:5397)
  • [4] P. Robba and A. Escassut, Prolongement analytique et algèbres de Banach ultrametrique, Astérisque 10, Soc. Math. France, 1973. MR 0354244 (50:6726)
  • [5] M. Waldschmidt, Nombres transcendants, Lecture Notes in Math., vol. 402, Springer-Verlag, Berlin, 1974. MR 0360483 (50:12931)

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Keywords: Schwarz's lemma, Schneider-Lang theorem
Article copyright: © Copyright 1980 American Mathematical Society

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