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On approximation with algebraic numbers of bounded degree
Published online by Cambridge University Press: 26 February 2010
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In this paper we are interested in two related measures of the degree of approximation of a complex number ζ by algebraic numbers. For a given integer n ≥ 1, write wn(ζ) for the supremum of the exponents w for which
for infinitely many polynomials
in Z[x] of height H(P) = max |av|. Clearly 0 ≤ w1 (ζ) ≤ w2 (ζ) ≤ …. On the other hand, write for the supremum of the exponents w for which
for infinitely many algebraic numbers α of degree at most n.
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