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Irrationalité de certaines sommes de séries

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Let \(q \in {\mathbb{Z}}\) with |q| > 1, and a be a rational number such that a 2 is not equal to \(\frac{(q^m+1)^2}{q^m}\) for \(m \in {\mathbb{Z}}\) . In this note, we prove that the sum \(\sum\nolimits_{n\geq 1}\frac{q^n}{q^{2n}+aq^n+1}\) is irrational.

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  1. Département de Mathématiques et Mécanique, Laboratoire N.Oresme, Université de Caen, Campus II, Boulevard du Maréchal Juin, BP 5186, 14032, Caen Cedex, France

    Jean-Paul Bézivin

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  1. Jean-Paul Bézivin
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Correspondence to Jean-Paul Bézivin.

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Bézivin, JP. Irrationalité de certaines sommes de séries. manuscripta math. 126, 41–47 (2008). https://doi.org/10.1007/s00229-007-0159-2

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  • DOI: https://doi.org/10.1007/s00229-007-0159-2

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