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- W4297776125 abstract "Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $gamma$. It involves similar linear combinations of logarithm numbers $L_{n,m}$. To prove that $gamma$ is irrational, it suffices to prove that, for some fixed $m$, the distance of $d_n L_{n,m}$ ($d_n$ is the least common multiple of the $n$ first integers) to the set of integers $mathbf{Z}$ does not converge to 0. A similar result is obtained by replacing logarithms numbers by rational numbers: it gives a sufficient condition involving only rational numbers. Unfortunately, the chaotic behavior of $d_n$ is an obstacle to verify this sufficient condition. All the proofs use in a large manner the theory of Pad'e approximation." @default.
- W4297776125 created "2022-10-01" @default.
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- W4297776125 date "2005-07-12" @default.
- W4297776125 modified "2023-09-26" @default.
- W4297776125 title "A family of criteria for irrationality of Euler's constant" @default.
- W4297776125 doi "https://doi.org/10.48550/arxiv.math/0507231" @default.
- W4297776125 hasPublicationYear "2005" @default.
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