Segre's theorem on asymmetric diophantine approximation

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود 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

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

Dirichlet’s Theorem on Diophantine Approximation and Homogeneous Flows

Given an m×n real matrix Y , an unbounded set T of parameters t = (t1, . . . , tm+n) ∈ R m+n + with ∑m i=1 ti = ∑n j=1 tm+j and 0 < ε ≤ 1, we say that Dirichlet’s Theorem can be ε-improved for Y along T if for every sufficiently large t ∈ T there are nonzero q ∈ Z and p ∈ Z such that { |Yiq− pi| < εe −ti , i = 1, . . . ,m |qj | < εe tm+j , j = 1, . . . , n (here Y1, . . . , Ym are rows of Y ). ...

متن کامل

Diophantine Approximation on Veech

— We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an ...

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: Journal of Number Theory

سال: 1988

ISSN: 0022-314X

DOI: 10.1016/0022-314x(88)90122-9