The author improves previously known results on the irrationality and the nonquadraticity measures of logarithms of suitable rational numbers. The previous record for the irrationality measure of log 2 was due to Rukhadze, who obtained in 1987 the upper bound 3.891...; here I obtain 3.574..., after more than twenty years of unsuccessful attempts of improving Rukhadze's record. As to nonquadraticity measures, a similar improvement, upon an earlier result by Hata in 2000, is obtained in this paper. Ideas from Sorokin, Hata and Rhin-Viola are combined.
The Rhin-Viola method for log 2
MARCOVECCHIO, RAFFAELE DARIO
2009-01-01
Abstract
The author improves previously known results on the irrationality and the nonquadraticity measures of logarithms of suitable rational numbers. The previous record for the irrationality measure of log 2 was due to Rukhadze, who obtained in 1987 the upper bound 3.891...; here I obtain 3.574..., after more than twenty years of unsuccessful attempts of improving Rukhadze's record. As to nonquadraticity measures, a similar improvement, upon an earlier result by Hata in 2000, is obtained in this paper. Ideas from Sorokin, Hata and Rhin-Viola are combined.File in questo prodotto:
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