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Irrationality exponents of generalized Hone series

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Abstract

We compute the exact irrationality exponents of certain series of rational numbers, first studied in a special case by Hone, by transforming them into suitable continued fractions.

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References

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Acknowledgements

The last named author was supported by the Research Institute for Mathematical Sciences, an International Joint Usage / Research Center located in Kyoto University. We thank the anonymous reviewer for giving valuable comments.

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Authors and Affiliations

  1. Baggio Engineering School, Lille, France

    Daniel Duverney

  2. Department of Applied Mathematics, Faculty of Science, Tokyo University of Science, Shinjuku, Japan

    Takeshi Kurosawa

  3. Department of Mathematics, Keio University, Yokohama, Japan

    Iekata Shiokawa

Authors
  1. Daniel Duverney
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  2. Takeshi Kurosawa
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  3. Iekata Shiokawa
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Corresponding author

Correspondence to Takeshi Kurosawa.

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Communicated by Adrian Constantin.

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Duverney, D., Kurosawa, T. & Shiokawa, I. Irrationality exponents of generalized Hone series. Monatsh Math 193, 291–303 (2020). https://doi.org/10.1007/s00605-020-01423-6

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  • DOI: https://doi.org/10.1007/s00605-020-01423-6

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