Metric Diophantine approximation on homogeneous varieties
نویسندگان
چکیده
منابع مشابه
A Note on Metric Inhomogeneous Diophantine Approximation
An inhomogeneous version of a general form of the Jarn k-Besicovitch Theorem is proved. Dedicated to Professor F. Chong for his 80th birthday 1. Introduction In some respects, inhomogeneous Diophantine approximation is rather diierent from homogeneous Diophantine approximation. Results in the former, where the additional variables ooer extràdegrees of freedom', are sometimes sharper or easier t...
متن کاملClassical metric Diophantine approximation revisited
The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation, a branch of Number Theory which draws on a rich and broad variety of mathematics. We discuss some recent progress and open problems concerning this classica...
متن کاملMetric Diophantine Approximation and Probability
Let pn qn pn qn x denote the nth simple continued fraction convergent to an arbitrary irrational number x De ne the sequence of approximation constants n x q njx pn qnj It was conjectured by Lenstra that for almost all x lim n n jfj j n and j x zgj F z where F z z log if z and log z log z if z This was proved in BJW and extended in Nai to the same conclusion for kj x where kj is a sequence of p...
متن کاملDiophantine 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...
متن کاملFlows on Homogeneous Spaces and Diophantine Approximation on Manifolds
We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. G. Sprindžuk in 1964. We also prove several related hypotheses of Baker and Sprindžuk formulated in 1970...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2014
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x13007859