Inhomogeneous Diophantine approximation in the coprime setting
نویسندگان
چکیده
منابع مشابه
Inhomogeneous approximation by coprime integers
This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α ∈ R and for any γ ∈ R and > 0 there are infinitely many pairs of coprime integers m,n such that |nα−m− γ| ≤ 1/|n| . This improves upon previously known results, in which the exponent of approximat...
متن کاملExponents of 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 exponent of approximation to a generic point in R n by a system of n linear forms is equal to the inverse of the uniform homogeneous exponent associate...
متن کاملInhomogeneous Non-linear Diophantine Approximation
Let be a strictly positive monotonically decreasing function deened on the set of positive integers. Given real numbers and , consider the solubility of the following two inequalities jq + pj < (q); (1) jq + p + j < (q) (2) for integers p and q. The rst problem is said to be homogeneous and the second inho-mogeneous (see 2]). The well known theorem of Khintchine 2, 4] asserts that for almost al...
متن کاملA Note on Metric Inhomogeneous Diophantine Approximation
An inhomogeneous version of a general form of the Jarn k-Besicovitch Theorem is proved. Dedicated to Professor F. Chong for his 80th birthday 1. Introduction In some respects, inhomogeneous Diophantine approximation is rather diierent from homogeneous Diophantine approximation. Results in the former, where the additional variables ooer extràdegrees of freedom', are sometimes sharper or easier t...
متن کاملSimultaneous inhomogeneous Diophantine approximation on manifolds
In 1998, Kleinbock & Margulis [KM98] established a conjecture of V.G. Sprindzuk in metrical Diophantine approximation (and indeed the stronger Baker-Sprindzuk conjecture). In essence the conjecture stated that the simultaneous homogeneous Diophantine exponent w0(x) = 1/n for almost every point x on a non-degenerate submanifold M of Rn. In this paper the simultaneous inhomogeneous analogue of Sp...
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: Advances in Mathematics
سال: 2019
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106773