Effective measures of irrationality for certain algebraic numbers

Michael A. Bennett
1997 Journal of the Australian Mathematical Society  
In this paper, we derive a number of explicit lower bounds for rational approximation to certain cubic irrationalities, proving, for example, that 1 _,< for any non-zero integers p and q. A number of these irrationality measures improve known results, including those for -^5, s/l and s/T\. Some Diophantine consequences are briefly discussed. 1991 Mathematics subject classification (Amer. Math. Soc): primary 11J68, 11J82; secondary 11D25, 11Y50, 11Y65.
doi:10.1017/s144678870000104x fatcat:myhyau2a3zacnjq2jnqohb47em