Results 31 to 40 of about 1,648,333 (245)

On the size of Diophantine m-tuples in imaginary quadratic number rings

Bulletin of Mathematical Sciences, 2021
A Diophantine m-tuple is a set of m distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers.
Nikola Adžaga
doaj   +1 more source

Littlewood and Duffin–Schaeffer-Type Problems in Diophantine Approximation [PDF]

Memoirs of the American Mathematical Society, 2020
Gallagher’s theorem describes the multiplicative diophantine approximation rate of a typical vector. We establish a fully inhomogeneous version of Gallagher’s theorem, a diophantine fibre refinement, and a sharp and unexpected threshold for Liouville ...
Sam Chow, Niclas Technau
semanticscholar   +1 more source

A theorem on diophantine approximations

Lietuvos Matematikos Rinkinys, 1998
A result is proved on approximation of irrational numbers by rational ones, satisfying some requirements on their multiplicative structure. The statement is comparable with that one on diophantine approximations with square-free integers.
Vilius Stakėnas
doaj   +3 more sources

On the metric theory of inhomogeneous Diophantine approximation: An Erdős-Vaaler type result [PDF]

Journal of Number Theory, 2020
In 1958, Szusz proved an inhomogeneous version of Khintchine's theorem on Diophantine approximation. Szusz's theorem states that for any non-increasing approximation function $\psi:\mathbb{N}\to (0,1/2)$ with $\sum_q \psi(q)=\infty$ and any number ...
Han Yu
semanticscholar   +1 more source

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Axioms, 2021
Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs),
Masooma Raza Hashmi, Syeda Tayyba Tehrim, Muhammad Riaz, Dragan Pamucar, Goran Cirovic   +4 more
doaj   +1 more source

Birational Nevanlinna Constants, Beta Constants, and Diophantine Approximation to Closed Subschemes [PDF]

Journal de Théorie des Nombres de Bordeaux, 2020
In an earlier paper (joint with Min Ru), we proved a result on diophantine approximation to Cartier divisors, extending a 2011 result of P. Autissier. This was recently extended to certain closed subschemes (in place of divisors) by Ru and Wang.
Paul Vojta
semanticscholar   +1 more source

Diophantine Approximations on Fractals [PDF]

Geometric and Functional Analysis, 2011
ISSN:1420 ...
Einsiedler, Manfred, Fishman, Lior, Shapira, Uri   +2 more
openaire   +4 more sources

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

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

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