Abstract:
The Hermite–Padé approximants for systems of functions, containing ln(1+1/z)ln(1−1/z) are considered. The research is motivated by the number-theoretic applications related to Diophantine approximations for products of logarithms. Two constructions are considered, for which it is possible to find an explicit form of Hermite–Padé approximants. Their asymptotic behavior is studied and convergence is proved.
\Bibitem{Lys17}
\by V.~G.~Lysov
\paper On Hermite--Pad\'e approximants for the product of two logarithms
\jour Keldysh Institute preprints
\yr 2017
\papernumber 141
\totalpages 24
\mathnet{http://mi.mathnet.ru/ipmp2359}
\crossref{https://doi.org/10.20948/prepr-2017-141}
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https://www.mathnet.ru/eng/ipmp2359
https://www.mathnet.ru/eng/ipmp/y2017/p141
This publication is cited in the following 2 articles:
A. V. Komlov, R. V. Palvelev, “Zeros of discriminants constructed from Hermite–Padé polynomials of an algebraic function and their relation to branch points”, Sb. Math., 215:12 (2024), 1633–1665
V. G. Lysov, “O diofantovykh priblizheniyakh proizvedeniya logarifmov”, Preprinty IPM im. M. V. Keldysha, 2018, 158, 20 pp.
Citation in format AMSBIB
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