Diophantine approximation by algebraic hypersurfaces and varieties
نویسندگان
چکیده
منابع مشابه
Diophantine Approximation by Algebraic Hypersurfaces and Varieties
Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about “approximation” to a point in Rn by hyperplanes defined over the rationals. That is, we seek hyperplanes with small distance from the given point. On the other hand, following Wirsing, we may ask about approximation to a real number by real algebraic numbers of degree at...
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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...
متن کاملDiophantine approximation by conjugate algebraic numbers
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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The first topic of the workshop, Diophantine approximation, has at its core the study of rational numbers which closely approximate a given real number. This topic has an ancient history, going back at least to the first rational approximations for π. The adjective Diophantine comes from the third century Hellenistic mathematician Diophantus, who wrote an influential text solving various equati...
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In this paper, we associate an invariant αx(L) to an algebraic point x on an algebraic variety X with an ample line bundle L. The invariant α measures how well x can be approximated by rational points on X , with respect to the height function associated to L. We show that this invariant is closely related to the Seshadri constant ǫx(L) measuring local positivity of L at x, and in particular th...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2006
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-06-04014-1