منابع مشابه
Report 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 کاملSome Remarks on Diophantine Approximations
BY P. ERDOS, University of Syracuse . [Received 27 July, 1948 .] 1 . The present note contains some disconnected remarks on diophatine approximations . First we collect a few well-known results about continued fractions, which we shall use later' . Let a be an irrational number, q, < q2 < . . . be the sequence of the denominators of its convergents . For almost all a we have fork > k,,(a), qk+,...
متن کاملDiophantine 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 کاملProblems and results on diophantine approximations
The older literature on this subject (until about 1935) is treated in the excellent book of Koksma [1] . The more recent literature is discussed in a very interesting paper of Cigler and Helmberg [2] . Unlike the above authors I by no means aim to cover the literature completely and will mostly discuss only problems on which I myself worked thus a more exact title would have been "Problems and ...
متن کاملQuantitative Diophantine Approximations on Projective Varieties
In this note we study some aspects of a paper of G. Faltings and G. Wüstholz [7]. In particular, we work out a quantitative version of their main theorem. Our result even gives an explicit presentation of the structure for the exceptional subspaces of [24]. For a generic projective variety we obtain double exponential estimates. However, knowing more about the geometry of the given variety one ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1961
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1961-0121357-5