Remarks on the theory of diophantine approximation
نویسندگان
چکیده
منابع مشابه
Some remarks on diophantine equations and diophantine approximation
We give many equivalent statements of Mahler’s generalization of the fundamental theorem of Thue. In particular, we show that the theorem of Thue–Mahler for degree 3 implies the theorem of Thue for arbitrary degree ≥ 3, and we relate it with a theorem of Siegel on the rational integral points on the projective line P(K) minus 3 points. Classification MSC 2010: 11D59; 11J87; 11D25
متن کاملIntrinsic Diophantine Approximation on Manifolds: General Theory
We investigate the question of how well points on a nondegenerate k-dimensional submanifold M ⊆ Rd can be approximated by rationals also lying on M , establishing an upper bound on the “intrinsic Dirichlet exponent” for M . We show that relative to this exponent, the set of badly intrinsically approximable points is of full dimension and the set of very well intrinsically approximable points is...
متن کاملNevanlinna Theory and Diophantine Approximation
As observed originally by C. Osgood, certain statements in value distribution theory bear a strong resemblance to certain statements in diophantine approximation, and their corollaries for holomorphic curves likewise resemble statements for integral and rational points on algebraic varieties. For example, if X is a compact Riemann surface of genus > 1, then there are no non-constant holomorphic...
متن کاملIntersection Theory and Diophantine Approximation
A keystone in the classical theory of diophantine approximation is the construction of an auxilliary polynomial. The polynomial is constructed so that it is forced (for arithmetic reasons) to vanish at certain approximating points and this contradicts an upper bound on the order of vanishing obtained by other (usually geometric) techniques; the contradiction then allows one to prove finiteness ...
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 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: Colloquium Mathematicum
سال: 1958
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-6-1-119-126