Results 81 to 90 of about 22,960 (196)

Distribution of integer points on determinant surfaces and a mod‐p analogue

Mathematika, Volume 72, Issue 2, April 2026.
Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley   +1 more source

Hausdorff dimension of sets arising in Diophantine approximation [PDF]

Kodai Mathematical Journal, 1996
A generalization of a result of \textit{I. Borosh} and \textit{A. S. Fraenkel} on restricted diophantine approximation [Nederl. Akad. Wet., Proc., Ser. A 75, 193-201 (1972; Zbl 0242.10014)] is obtained. Given a non-negative function \(g:\mathbb{N}\to \mathbb{R}_{\geq 0}\), let \(C_\alpha(N)=|\{q\leq N:g(q)\geq q^{-\alpha}\}|\) and let \(\gamma(\alpha)=
Hinokuma, Takanori, Shiga, Hiroo
openaire   +2 more sources

Ill-distributed sets over global fields and exceptional sets in diophantine geometry [PDF]

Acta Arithmetica, 2021
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that for definable sets $X$ in $\mathbb{R}_{\exp}$ of dimension at most $2$ a conjecture of Wilkie about the density of rational points is equivalent to the fact that $X$ is badly distributed at the level of residue classes for many primes of $K$.
openaire   +2 more sources

Diophantine property in the group of affine transformations of the line

, 2013
We investigate the Diophantine property of a pair of elements in the group of affine transformations of the line. We say that a pair of elements g_1,g_2 in this group is Diophantine if there is a number A such that a product of length l of elements of ...
Varjú, Péter Pál
core   +1 more source

f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials

Mathematika, Volume 72, Issue 2, April 2026.
Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
wiley   +1 more source

F-Diophantine sets over finite fields

International Journal of Number Theory
Let [Formula: see text], q be an odd prime power, and [Formula: see text] be a polynomial. An F-Diophantine set over a finite field [Formula: see text] is a set [Formula: see text] such that [Formula: see text] is a square in [Formula: see text] whenever [Formula: see text] are distinct elements in A.
Chi Hoi Yip, Semin Yoo
openaire   +3 more sources

Winning Sets, Quasiconformal Maps and Diophantine Approximation [PDF]

Geometric and Functional Analysis, 2010
The Schmidt game was introduced by \textit{W. M. Schmidt} in [Trans. Am. Math. Soc. 123, 178--199 (1966; Zbl 0232.10029)]. The game has two players, \(A\) and \(B\), who successively choose euclidean balls \[ B_1 \supset A_1 \supset B_2 \supset A_2 \supset \cdots, \] with diameters satisfying \(| A_i | = \alpha | B_i |\) and \(| B_{i+1} | = \beta | A_i|
openaire   +3 more sources

Tubular neighborhoods of nodal sets and diophantine approximation [PDF]

American Journal of Mathematics, 2009
We give upper and lower bounds on the volume of a tubular neighborhood of the nodal set of an eigenfunction of the Laplacian on a real analytic closed Riemannian manifold $M$. As an application we consider the question of approximating points on $M$ by nodal sets, and explore analogy with approximation by rational numbers.
Jakobson, Dmitry, Mangoubi, Dan
openaire   +2 more sources

A Novel Approach to Roughness of Linear Diophantine Fuzzy Sets by Fuzzy Relations and Its Application Toward Multi-Criteria Group Decision-Making

IEEE Access
The notion of linear Diophantine fuzzy sets (LD-FSs) is a novel mechanism to combat uncertainties in decision analysis. Due to reference parameters associated with membership grade (MG) and non-membership grade (NMG), LD-FS is more efficient and reliable
Saba Ayub, Rizwan Gul, Muhammad Shabir, Ali Yahya Hummdi, Amer Aljaedi, Zaid Bassfar   +5 more
doaj   +1 more source

A Nonperturbative Eliasson's Reducibility Theorem

, 2005
This paper is concerned with discrete, one-dimensional Schr\"odinger operators with real analytic potentials and one Diophantine frequency. Using localization and duality we show that almost every point in the spectrum admits a quasi-periodic Bloch wave ...
Aizenman M, Arnol′d V I, Aubry S André G, Avila A, Avila A Jitomirskaya S, Avron J, Bourgain J, Bourgain J, Bourgain J, Chulaevsky V, Chulaevsky V A, Coppel W A, Datta S, De Concini C, Deift P, Delyon F, Dinaburg E I, Eliasson L H, Gordon A Y, Herman M R, Ince E L, Janot C, Jitomirskaya S, Jitomirskaya S, Jitomirskaya S Ya, Joaquim Puig, Johnson R, Johnson R, Johnson R, Johnson R, Johnson R A, Ketoja J A, Krikorian R, Last Y, Moser J, Moser J, Núñez C, Puig J, Puig J, Puig J, Riedel N, Simon B, Simon B, Sinai Ya G, Sinai Ya G, Sorets E   +45 more
core   +2 more sources