Symmetrized polynomials in a problem of estimating the irrationality measure of the number \(\ln 3\). (Russian. English summary) Zbl 1439.11171
Let \(h_1\), \(h_2\) and \(h\) be integers. Set \(H= \max (\vert h_1\mid ,\mid h_1\vert)\). Then the authors prove that there exists a positive integer \(H_0\) such that if \(H>H_0\) then
\[ \vert h_1\ln 2+h_2\ln 3+h\vert >h^{4.116201}. \]
From this we obtain that for the irrationality measure of \(\ln 3\) we have \(\mu(\ln 3)\leq 5.116201\)
The proof is interesting and made use special polynomials and rational functions
\[ \vert h_1\ln 2+h_2\ln 3+h\vert >h^{4.116201}. \]
From this we obtain that for the irrationality measure of \(\ln 3\) we have \(\mu(\ln 3)\leq 5.116201\)
The proof is interesting and made use special polynomials and rational functions
Reviewer: Jaroslav Hančl (Ostrava)
MSC:
| 11J82 | Measures of irrationality and of transcendence |
Keywords:
Diophantine approximations; irrationality measure; symmetrized polynomials; linear independenceReferences:
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