Simultaneous approximation of a real number by all conjugates of an algebraic number

Details Simultaneous approximation of a real number by all conjugates of an algebraic number Simultaneous approximation of a real number by all conjugates of an algebraic number

2007-06-07

arxiv.org/abs/0706.1022v1

Acta Arith. 127 (2007), 63-70

Mathematics

Number Theory

7 pages

Scientific paper

Using a method of H. Davenport and W. M. Schmidt, we show that, for each
positive integer n, the ratio 2/n is the optimal exponent of simultaneous
approximation to real irrational numbers 1) by all conjugates of algebraic
numbers of degree n, and 2) by all but one conjugates of algebraic integers of
degree n+1.

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