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Subspace Lang conjecture and some remarks on a transcendental criterion

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Abstract

Let \(b\ge 2\) be an integer and \(\alpha \) is a non-zero real number written in b-ary expansion. Adamczewski et al. (C. R. Acad. Sci. Paris 339 (2004) 11–14) provided a criterion for an irrational number to be a transcendental number using b-ary expansion. In this paper, we make some remarks on this criterion and, under the assumption of Subspace Lang Conjecture, we extend this criterion for a much wider class of irrational numbers.

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Acknowledgements

The authors are thankful to their Ph.D. advisor, R Thangadurai for fruitful discussions and for carefully going through the paper. They would also like to acknowledge the Department of Atomic Energy, Govt. of India for providing a research grant. The second author was supported in part by the ’INFOSYS’ scholarship for senior students at HRI, Allahabad. The authors also wish to thank the referee for going through the manuscript meticulously.

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  1. Harish-Chandra Research Institute (HBNI), Chhatanag Road, Jhunsi, Allahabad, 211 019, India

    Veekesh Kumar & Nabin Kumar Meher

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  1. Veekesh Kumar
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  2. Nabin Kumar Meher
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Correspondence to Veekesh Kumar.

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Communicating Editor: B Sury

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Kumar, V., Meher, N.K. Subspace Lang conjecture and some remarks on a transcendental criterion. Proc Math Sci 128, 30 (2018). https://doi.org/10.1007/s12044-018-0413-4

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  • DOI: https://doi.org/10.1007/s12044-018-0413-4

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