منابع مشابه
Diophantine Approximations, Diophantine Equations, Transcendence and Applications
This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...
متن کاملDiophantine and Ergodic Foliations on Surfaces
This paper gives a topological characterization of Diophantine and recurrent laminations on surfaces. It also establishes an upper bound for the number of ergodic components of a measured foliation, in terms of limits of the corresponding geodesic ray in Mg,n. Taken together, these results give a new approach to Masur’s theorem on unique ergodicity. Teichmüller rays. Let Mg,n denote the moduli ...
متن کاملDiophantine Approximations and Toric Deformations
1.1. Let S be a finite set of places of a finite field extension L of a number field K, containing all infinite places. Let E be a vector space over K of dimension N + 1. For v ∈ S, let lv0, · · · , lvN be linearly independent vectors in E ⊗K L. Choose a projective subvariety X defined over K, embedded into the projective space P(E∨) of lines of the dual vector space E∨. Consider the system of ...
متن کاملReport on Diophantine approximations
© Bulletin de la S. M. F., 1965, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
متن کاملThe best Diophantine approximations: the
This brief survey deals with multi-dimensional Diophantine approximations in sense of linear form and with simultaneous Diophantine approximations. We discuss the phenomenon of degenerate dimension of linear sub-spaces generated by the best Diophantine approximations. Originally most of these results have been established by the author in [14, 15, 16, 17, 18]. Here we collect all of them togeth...
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ژورنال
عنوان ژورنال: Publications mathématiques de l'IHÉS
سال: 1998
ISSN: 0073-8301,1618-1913
DOI: 10.1007/bf02698862