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Archiv der Mathematik

, Volume 102, Issue 1, pp 59–70 | Cite as

Liouville numbers and Schanuel’s Conjecture

  • K. Senthil Kumar
  • R. Thangadurai
  • M. Waldschmidt
Article

Abstract

In this paper, using an argument of P. Erdős, K. Alniaçik, and É. Saias, we extend earlier results on Liouville numbers, due to P. Erdős, G.J. Rieger, W. Schwarz, K. Alniaçik, É. Saias, E.B. Burger. We also produce new results of algebraic independence related with Liouville numbers and Schanuel’s Conjecture, in the framework of \({G_\delta}\) -subsets.

Keywords

Nonempty Interior Zero Function Transcendence Degree Nonempty Open Subset Binary Expansion 
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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • K. Senthil Kumar
    • 1
  • R. Thangadurai
    • 1
  • M. Waldschmidt
    • 2
  1. 1.Harish-Chandra Research InstituteAllahabadIndia
  2. 2.Institut de Mathématiques de Jussieu, Théorie des Nombres Case courrier 247Université Pierre et Marie Curie (Paris 6)Paris Cedex 05France

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