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ON THE TRANSCENDENCE OF CERTAIN REAL NUMBERS

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  20 February 2019

VEEKESH KUMAR Open the ORCID record for VEEKESH KUMAR [Opens in a new window]  and
BILL MANCE Open the ORCID record for BILL MANCE [Opens in a new window]
VEEKESH KUMAR
Affiliation:
Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad – 211019, India email [email protected]
BILL MANCE*
Affiliation:
Uniwersytet im. Adama Mickiewicza w Poznaniu, Collegium Mathematicum, ul. Umultowska 87, 61-614 Poznań, Poland email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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In this article, we prove the transcendence of certain infinite sums and products by applying the subspace theorem. In particular, we extend the results of Hančl and Rucki [‘The transcendence of certain infinite series’, Rocky Mountain J. Math.35 (2005), 531–537].

Keywords

transcendencerational approximationsubspace theorem

MSC classification

Primary: 11J68: Approximation to algebraic numbers
Secondary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 3 , June 2019 , pp. 392 - 402
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was supported by a research grant from the Department of Atomic Energy, Government of India.

References

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