Diophantine approximation by conjugate algebraic integers
نویسندگان
چکیده
منابع مشابه
Diophantine approximation by conjugate algebraic integers
Building on the work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel’fond’s transcendence criterion which provides a sufficient condition for a complex or p-adic number ξ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at ξ together with most of their derivatives. The second one, which follows from this crit...
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In 1969, Davenport and Schmidt provided upper bounds for the approximation of a real number by algebraic integers. Their novel approach was based on the geometry of numbers and involved the duality for convex bodies. In the present thesis we study the approximation of a real number by conjugate algebraic numbers. We find inspiration in Davenport and Schmidt’s method, but ultimately our approxim...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2004
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x03000708