Homogeneous Diophantine approximation inS-integers

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

Diophantine approximation by conjugate algebraic integers

Building on the work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel’fond’s transcendence criterion which provides a sufficient condition for a complex or p-adic number ξ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at ξ together with most of their derivatives. The second one, which follows from this crit...

متن کامل

Flows on Homogeneous Spaces and Diophantine Approximation on Manifolds

We present a new approach to metric Diophantine approximation on manifolds based on the correspondence between approximation properties of numbers and orbit properties of certain flows on homogeneous spaces. This approach yields a new proof of a conjecture of Mahler, originally settled by V. G. Sprindžuk in 1964. We also prove several related hypotheses of Baker and Sprindžuk formulated in 1970...

متن کامل

On Exponents of Homogeneous and Inhomogeneous Diophantine Approximation

In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the inhomogeneous exponent of approximation to a generic point in R by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent...

متن کامل

Diophantine Approximation, Flows on Homogeneous Spaces and Counting

Let ξ ∈ R, let ι : [1,∞)→ (0, 1] be a positive decreasing function, and let E ξ (ι, Q) be the set of integer pairs (p, q) satisfying |p + qξ| < ι(q), 0 < q < Q. In a series of papers starting in 1959 Erdős [14], Schmidt [22, 23], Lang [18, 19, 9], Adams [1, 2, 3, 4, 5, 7, 6, 8], Sweet [26], and others, considered the problem of finding the asymptotics for the cardinality |E ξ (ι, Q)| as Q gets ...

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

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: Pacific Journal of Mathematics

سال: 1992

ISSN: 0030-8730,0030-8730

DOI: 10.2140/pjm.1992.152.211