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Journal of the London Mathematical Society 2002 65(3):547-559; doi:10.1112/S0024610702003137
© 2002 by London Mathematical Society
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© The London Mathematical Society

Approximation by Algebraic Integers and Hausdorff Dimension

Yann Bugeaud

UFR de Mathématiques, Université Louis Pasteur 7 rue René Descartes, 67084 Strasbourg Cedex, France, bugeaud{at}math.u-strasbg.fr

Received 11 December 2000. Revision received 14 September 2001.

The paper computes the Hausdorff dimension of sets of real numbers which are close to infinitely many real algebraic integers of bounded degree. It also investigates the distribution of real algebraic integers of bounded degree, which are proved to be evenly spaced.


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