Distances between the conjugates of an algebraic number

Details Distances between the conjugates of an algebraic number Distances between the conjugates of an algebraic number

2004-08-23

arxiv.org/abs/math/0408304v1

Mathematics

Number Theory

Latex file; 18 pages

Scientific paper

Given a fixed number field K, we give non-trivial lower bounds for the
distance between the conjugates of any number a from K in terms of the Mahler
measure M(a) of a. In the case that K is a cubic field, our bound is best
possible in terms of M(a). Our proof is based on Roth's theorem.

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