Results 131 to 140 of about 1,648,333 (245)

From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges

Discrete Analysis, 2017
From a packing problem to quantitative recurrence in [0,1] and the Lagrange spectrum of interval exchanges, Discrete Analysis 2017:10, 25 pp. A basic fact in the theory of Diophantine approximation is Dirichlet's theorem that for every real number ...
Michael Boshernitzan, Vincent Delecroix
doaj   +1 more source

Metrical Diophantine approximation for quaternions [PDF]

, 2014
Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup ...
Everitt, Brent, Dodson, Maurice
core   +1 more source

Successful cryptanalysis on RSA type modulus N=p2q

e-Prime: Advances in Electrical Engineering, Electronics and Energy
As internet technology advances and our interactions increasingly take place online, cryptography emerges as a valuable tool to address security concerns. Cryptography serves as a means to guarantee the protection of privacy and confidential information,
Normahirah Nek Abd Rahman
doaj   +1 more source

Sequences of Diophantine approximations

Journal of Number Theory, 1974
AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free sequences of “good” Diophantine approximations to a fixed α ∈ C are trivial ones. For example, suppose that a > 1 and that (δn)n=1∞ and (σn)n=1∞ are two positive, strictly increasing unbounded sequences satisfying δn+1 ≤ aδn and σn+1 ≤ aσn.
openaire   +1 more source

A Diophantine equation appearing in Diophantine approximation [PDF]

, 2001
All Diophantine equations ax2 + by2 + cz2 = 1 + dxyz, with a, b, c, d ∈ N and a|d, b|d, c|d, having solutions (x, y, z) ∈ N3 are determined. One particular equation of this type 2x2 + 2y2 + 3z2 = 1 + 6xyz appeared recently in connection with the ...
Schmidt, Asmus L., Jin, Yuan
core   +1 more source

Inhomogeneous Diophantine Approximation [PDF]

, 2018
Diophantine approximation is a topic of number theory concerned with rational approximations of real, typically irrational, numbers. In other words, we seek q∈Z for a given α∈R such that ||qα|| (the distance from qα to the nearest integer) is small. This
King, Brian., King, Brian
core   +1 more source

Remarks on Diophantine approximation in function fields

, 2019
We study some problems in metric Diophantine approximation over local fields of positive ...
Ganguly, Arijit, Ghosh, Anish
core   +2 more sources

Diophantine Approximation, Lagrange and Markov Spectra, and Dynamical Cantor Sets

, 2021
C. Matheus, C. Moreira
semanticscholar   +1 more source

DIOPHANTINE APPROXIMATION FOR ALGEBRAIC POINTS ON CURVES

, 2020
A foundational result in Diophantine approximation is Roth's theorem, which asserts that for a given algebraic number $\alpha$ and $\varepsilon>0$, the inequality $|\alpha-p/q| 0$, we get\[m_{D,S}(P)\leq (N_d(D)+\varepsilon) h_R(P) +O(1)\]for all $P\in C(
Plante, Thomas
core   +1 more source

The approximate functional equation of some Diophantine series. [PDF]

Mon Hefte Math, 2023
Chamizo F, Martin B.
europepmc   +1 more source