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Acta Mathematica Hungarica

, Volume 159, Issue 1, pp 265–286 | Cite as

A note on the arithmetic nature of some infinite series

  • N. K. MeherEmail author
Article
  • 39 Downloads

Abstract

Weatherby [14] studied some infinite series and proved that they are either zero or transcendental. Here, we extend his results. Moreover, we find a linear independence criteria of these series under some mild conditions.

Key words and phrases

transcendental number infinite series Nesterenko’s theorem linear independence 

Mathematics Subject Classification

11J81 11J72 

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Notes

Acknowledgements

I am grateful to the anonymous referee for useful and helpful remarks and comments which improved the presentation of the manuscript. I am thankful to my Ph.D. advisor Professor R. Thangadurai for carefully going through the paper. The part of the work was done during my stay at Harish -Chandra Research Institute, Allahabad, India.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesNational Institute of Science Education and Research, Bhubaneswar, HBNIKhurdhaIndia

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