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Liouville numbers and Schanuel’s Conjecture

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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.

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Authors and Affiliations

  1. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India

    K. Senthil Kumar & R. Thangadurai

  2. Institut de Mathématiques de Jussieu, Théorie des Nombres Case courrier 247, Université Pierre et Marie Curie (Paris 6), Paris Cedex 05, France

    M. Waldschmidt

Authors
  1. K. Senthil Kumar
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  2. R. Thangadurai
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  3. M. Waldschmidt
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Correspondence to K. Senthil Kumar.

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Kumar, K.S., Thangadurai, R. & Waldschmidt, M. Liouville numbers and Schanuel’s Conjecture. Arch. Math. 102, 59–70 (2014). https://doi.org/10.1007/s00013-013-0606-0

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  • DOI: https://doi.org/10.1007/s00013-013-0606-0

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