Results 21 to 30 of about 12,497 (156)
Exceptional Sets for Diophantine Inequalities [PDF]
International Mathematics Research Notices, 2013 We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c.
Parsell, Scott T., Wooley, Trevor D.
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Observation of vibrating systems at different time instants
Electronic Journal of Qualitative Theory of Differential Equations, 2014 In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of A. Szijártó and J.
Ambroise Vest
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Local Diophantine Nullstellen inequalities [PDF]
Journal of the American Mathematical Society, 1988 The main result of this paper is as follows. Let \(P_1,\ldots, P_n\) be polynomials of total degree at most \(D\) in \(x_1,\ldots,x_m\), with rational integer coefficients of absolute values at most \(H\).
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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' sets.Comment: 30 pages.
Beresnevich +27 more
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Symmetric modular Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 2006 In this paper we study and characterize those Diophantine inequalities a x mod b ≤ x ax\operatorname {mod} b\leq x whose set of solutions is a symmetric numerical semigroup.
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Finiteness results for Diophantine triples with repdigit values [PDF]
, 2015 Let $g\ge 2$ be an integer and $\mathcal R_g\subset \mathbb N$ be the set of repdigits in base $g$. Let $\mathcal D_g$ be the set of Diophantine triples with values in $\mathcal R_g$; that is, $\mathcal D_g$ is the set of all triples $(a,b,c)\in \mathbb ...
Bérczes, Attila +3 more
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Proportionally modular diophantine inequalities
Journal of Number Theory, 2003 The authors study the sets of nonnegative solutions of Diophantine inequalities of the form \(ax\) mod \(b \leq cx\) with \(a, b\) and \(c\) positive integers. These sets are numerical semigroups, which are investigated and characterized.
Rosales, J.C. +3 more
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Central limit theorem and Diophantine approximations [PDF]
, 1910 Let $F_n$ denote the distribution function of the normalized sum $Z_n = (X_1 + \dots + X_n)/\sigma\sqrt{n}$ of i.i.d. random variables with finite fourth absolute moment.
Bobkov, Sergey G.
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One Cubic Diophantine Inequality [PDF]
Journal of the London Mathematical Society, 2000 Let \(F(x)\) be a cubic form with real coefficients in \(s\) variables. \textit{J. Pitman} [J. Lond. Math. Soc. 43, 119-126 (1968; Zbl 0164.05301)] proved that there exists \(s_0> 0\) such that for any \(s\geq s_0\) the inequality \[ |F(x)|< 1 \tag{1} \] is solvable in \({\mathbf x}\in \mathbb{Z}^3\setminus \{\mathbf{0}\}\). About the quantitative part,
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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
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