On the approximation of logarithms of algebraic numbers
Author:
- 15 January 1953
- journal article
- Published by The Royal Society in Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Vol. 245 (898) , 371-398
Abstract
A new identity is given by means of which infinitely many algebraic functions approximating the logarithmic function In x are obtained. On substituting numerical algebraic values for the variable, a lower bound for the distance of its logarithm from variable algebraic numbers is found. As a further application, it is proved that the fractional part of the number ea is greater than a-40a for every sufficiently large positive integer a.Keywords
This publication has 3 references indexed in Scilit:
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- Zur Approximation der Exponentialfunktion und des Logarithmus. Teil I.Journal für die reine und angewandte Mathematik (Crelles Journal), 1932
- Approximation algebraischer ZahlenMathematische Zeitschrift, 1921