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This article is cited in 17 scientific papers (total in 18 papers)
An effective refinement of the exponent in Liouville's theorem
N. I. Fel'dman
Abstract:
For every algebraic number $\alpha$ of degree $n\geqslant3$ there exist effective positive constants $a$ and $C$ such that for any rational integers $q>0$ and $p$ we have
$$
\biggl|\alpha-\frac pq\biggr|>Cq^{a-n}.
$$
We also derive an effective boundary of the type $C_1m^{a_1}$ for the solutions of the Diophantine equation $f(x,y)=m$, where $f$ is a form of degree $\geqslant3$.
Received: 18.02.1971
Citation:
N. I. Fel'dman, “An effective refinement of the exponent in Liouville's theorem”, Math. USSR-Izv., 5:5 (1971), 985–1002
Linking options:
https://www.mathnet.ru/eng/im2114https://doi.org/10.1070/IM1971v005n05ABEH001130 https://www.mathnet.ru/eng/im/v35/i5/p973
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