Dirichlet's diophantine approximation theorem

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Roth’s Theorem: an introduction to diophantine approximation

Indeed, P (p/q) is a sum of rational numbers whose denominators are all factors of q: expressing this as a rational number with denominator q, it is either identically zero or it is at is at least 1/q in absolute value because one is the smallest positive integer. Since |P (p/q)| is bounded below as a function of q, when it is non–zero, it follows from a continuity argument that p/q can not be ...

متن کامل

The Lagrange Theorem for Multidimensional Diophantine Approximation

In this paper we give a necessary and sufficient condition for z in the floor of the Poincaré half-space to have periodicity in the multidimensional Diophantine approximation by convergents using the Hermite algorithm. We examine in detail the structure of the corresponding sequences and give some examples

متن کامل

A Metric Theorem for Restricted Diophantine Approximation in Positive Characteristic

0 whenever ai = 0 for all i ∈ Z, k whenever an 6= 0 and ai = 0 for i < n. We can interpret F(X) as the completion of F(X) in this absolute value. Diophantine approximation in F(X), where a generic element is approximated by elements from the field of fractions F(X), has been studied by numerous authors (the survey papers [9, 11] contain some of the known results). Broadly speaking, the object o...

متن کامل

An Effective Version of Kronecker’s Theorem on Simultaneous Diophantine Approximation

Kronecker’s theorem states that if 1, θ1, . . . , θn are real algebraic numbers, linearly independent over Q, and if α ∈ R, then for any > 0 there are q ∈ Z and p ∈ Z such that |qθi − αi − pi| < . Here, a bound on q is given in terms of the dimension n, of the precision , of the degree of the θi’s and of their height. A possible connection to the square-root sum problem is discussed.

متن کامل

Classical metric Diophantine approximation revisited: the Khintchine-Groshev theorem

Let An,m(ψ) denote the set of ψ-approximable points in R mn. Under the assumption that the approximating function ψ is monotonic, the classical KhintchineGroshev theorem provides an elegant probabilistic criterion for the Lebesgue measure of An,m(ψ). The famous Duffin-Schaeffer counterexample shows that the monotonicity assumption on ψ is absolutely necessary when m = n = 1. On the other hand, ...

متن کامل

ذخیره 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: Bulletin of the Australian Mathematical Society

سال: 1977

ISSN: 0004-9727,1755-1633

DOI: 10.1017/s0004972700023224