1. Rational approximations to algebraic numbers
- Author
-
D. Ridout
- Subjects
Discrete mathematics ,symbols.namesake ,Function field of an algebraic variety ,Lindemann–Weierstrass theorem ,General Mathematics ,Rational point ,symbols ,Algebraic extension ,Algebraic function ,Field (mathematics) ,Algebraic number ,Algebraically closed field ,Mathematics - Abstract
It was proved by Roth in a recent paper that if α is any real algebraic number, and if K > 2, then the inequalityhas only a finite number of solutions in relatively prime integers p, q (q > 0) The object of the present paper is to prove that the lower bound for κ can be reduced if conditions are imposed on p and q. The result obtained is as follows.
- Published
- 1957