On the irrationality measure of \(\log 3\) (Q403297)

\textit{V. Kh. Salikhov} [Dokl. Math. 76, No. 3, 955--957 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 6, 753--755 (2007; Zbl 1169.11032)] proved that the irrationality measure of \(\log 3\) has an upper bound \(\mu(\log 3)<5.126\). In the present paper the authors improved Salikhov's method and found a better upper bound \(\mu(\log 3)<5.117\).NEWLINENEWLINEThis bound follows from a more general result stating that \(\left| p+q_1\log 2+q_2\log 3\right|>H^{-4.117}\) for every \(p,q_1,q_2\) with sufficiently large \(H=\max\{|q_1|,|q_2|\}\).NEWLINENEWLINEThe authors used semi-infinite linear programming and the LLL algorithm to find suitable polynomials appearing in the proof.