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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0577748-9
MathSciNet review: 577748
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Abstract | References | Similar Articles | Additional Information

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] Daniel 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. G18, Secrétariat Mathématique, Paris, 1975, pp. 13 (French). MR 0401661
  • [2] Daniel Bertrand, Séries d’Eisenstein et transcendance, Bull. Soc. Math. France 104 (1976), no. 3, 309–321. MR 0437468
  • [3] Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547
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  • [5] Michel Waldschmidt, Nombres transcendants, Lecture Notes in Mathematics, Vol. 402, Springer-Verlag, Berlin-New York, 1974 (French). MR 0360483

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577748-9
Keywords: Schwarz's lemma, Schneider-Lang theorem
Article copyright: © Copyright 1980 American Mathematical Society

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