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Preprints of the Keldysh Institute of Applied Mathematics, 2018, 158, 20 pp.
DOI: https://doi.org/10.20948/prepr-2018-158 (Mi ipmp2517) 		 
On Diophantine approximants for the product of logarithms

V. G. Lysov
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DOI: https://doi.org/10.20948/prepr-2018-158
Abstract: The approximation by rational fractions for the product of logarithms is considered. It is proved that the numbers $\ln(1-1/m) \ln(1+1/m)$ are irrational for all integers $m \geqslant 33$. New estimates for the irrationality measure of these numbers are obtained.
Keywords: Hermite–Padé approximants, Diophantine approximants, irrationality, irrationality measure.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00614_a
Bibliographic databases:
Document Type: Preprint
UDC: 517.53
Language: Russian
Citation: V. G. Lysov, “On Diophantine approximants for the product of logarithms”, Keldysh Institute preprints, 2018, 158, 20 pp.
Citation in format AMSBIB
\Bibitem{Lys18}
\by V.~G.~Lysov
\paper On Diophantine approximants for the product of logarithms
\jour Keldysh Institute preprints
\yr 2018
\papernumber 158
\totalpages 20
\mathnet{http://mi.mathnet.ru/ipmp2517}
\crossref{https://doi.org/10.20948/prepr-2018-158}
\elib{https://elibrary.ru/item.asp?id=35385338}
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