Results 41 to 50 of about 2,483 (259)

Diophantine approximation on curves and the distribution of rational points: Contributions to the divergence theory

, 2021
In this paper we develop an explicit method for studying the distribution of rational points near manifolds. As a consequence we obtain optimal lower bounds on the number of rational points of bounded height lying at a given distance from an arbitrary ...
V. Beresnevich, R. Vaughan, S. Velani, E. Zorin   +3 more
semanticscholar   +1 more source

Diophantine Approximation, Ostrowski Numeration and the Double-Base Number System [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
Analysis of ...
Valerie Berthe, Laurent Imbert
doaj   +1 more source

A note on the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 [PDF]

Notes on Number Theory and Discrete Mathematics
We prove that, for k≥10, the Diophantine equation (xᵏ-1)(yᵏ-1)²=zᵏ-1 in positive integers x, y, z, k with z>1, has no solutions satisfying ...
Yangcheng Li
doaj   +1 more source

Counting rationals and diophantine approximation in missing-digit Cantor sets [PDF]

Advances in Mathematics
We establish a new upper bound for the number of rationals up to a given height in a missing-digit set, making progress towards a conjecture of Broderick, Fishman, and Reich.
Sam Chow, P'eter P. Varj'u, Han Yu
semanticscholar   +1 more source

Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2001
The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux, Valerie Berthe, Hiromi Ei, Shunji Ito   +3 more
doaj   +1 more source

Diophantine Approximation and Diophantine Equations [PDF]

, 2018
P. Corvaja, U. Zannier
openaire   +2 more sources

Lower bounds for simultaneous Diophantine approximation constants [PDF]

, 2014
summary:After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $\theta _s$, new lower bounds are deduced for $\theta _6$ and $\theta _7$
Nowak, Werner Georg
core   +1 more source

A Zero-One Law for Uniform Diophantine Approximation in Euclidean Norm [PDF]

International mathematics research notices, 2019
We study a norm-sensitive Diophantine approximation problem arising from the work of Davenport and Schmidt on the improvement of Dirichlet’s theorem. Its supremum norm case was recently considered by the 1st-named author and Wadleigh [ 17], and here we
D. Kleinbock, Anurag Rao
semanticscholar   +1 more source

On asymmetric Diophantine approximations. [PDF]

Michigan Mathematical Journal, 1962
It is well known the following theorem of \textit{B. Segre} [Duke Math. J. 12, 337--365 (1945; Zbl 0060.11807)]: Every irrational number \(\theta\) has infinitely many rational approximations \(h/k\) satisfying: \[ -1/(1+4\tau)^{1/2} K^2 < \theta - h/k < \tau /(1+4 \tau)^{1/2} K^2 \] where \(\tau\) is any given non-negative real number.
openaire   +3 more sources

Diophantine approximation and deformation [PDF]

Bulletin de la Soci&#233;t&#233; math&#233;matique de France, 2000
We associate certain curves over function fields to given algebraic power series and show that bounds on the rank of Kodaira-Spencer map of this curves imply bounds on the exponents of the power series, with more generic curves giving lower exponents.
Kim, M, Thakur, D, Voloch, J
openaire   +4 more sources