Approximation of complex algebraic numbers by algebraic numbers of bounded degree

Details Approximation of complex algebraic numbers by algebraic numbers of bounded degree Approximation of complex algebraic numbers by algebraic numbers of bounded degree

2007-09-11

arxiv.org/abs/0709.1556v1

Mathematics

Number Theory

34 pages

Scientific paper

We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers are more badly approximable by algebraic integers of degree at most n+1 than almost all complex numbers.

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