Also, if [[alpha].sub.1], [[alpha].sub.2] are distinct

algebraic numbers conjugate over Q then

1e

algebraic numbers with grows of b have tendency became closer to rational maxima.

Our main results (Theorem 5 and Proposition 7) may seem surprising as we might expect that any

algebraic number would be computable in our setting.

An

algebraic number is one that can serve as a solution to a polynomial equation made up of x and powers of x.

Bugeaud introduces Bakers theory of linear forms in the logarithms of

algebraic numbers, with a special emphasis on a large variety of its applications, mainly to Diophantine questions.

Any non-vanishing linear combination of logarithms of

algebraic numbers with algebraic coefficients is transcendental.

This collection of Artin's work includes his books Galois Theory, The Gamma Function and The Theory of

Algebraic Numbers, and papers on the axiomatic characterization of fields with George Whaples, real fields ("A Characterization of the Field of Real

Algebraic Numbers," "The Algebraic Construction of Real Fields" and "A Characterization of Real Closed Fields") in their first English translation, and the theory of braids.

The lecture topics include quasiconformal mappings, Teichmiller spaces, and Kleinian groups; calcul infinitesimal stochastique; rational approximations to

algebraic numbers, and many others.

Artin, Theory of

algebraic numbers, Notes by Gerhard Wurges from lectures held at the Mathematisches Institut, Gottingen, Germany, in the Winter Semester, 1956/7, translated by George Striker, Schildweg 12, Goottingen, 1959.

In his text he covers

algebraic numbers, field extensions, minimal polynomials, multiply generated fields, and the Galois correspondence, closing with such classical topics as binomial equations and solvability in radicals.