Results 41 to 50 of about 788,130 (111)
On simultaneous diophantine approximations to $\zeta(2)$ and $\zeta(3)$
, 2013 The authors present a hypergeometric construction of rational approximations to $\zeta(2)$ and $\zeta(3)$ which allows one to demonstrate simultaneously the irrationality of each of the zeta values, as well as to estimate from below certain linear forms ...
Dauguet, Simon, Zudilin, Wadim
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Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
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From Diophantine approximations to Diophantine equations [PDF]
, 2016 : We consider the global generalization of the continued fraction giving the best Diophantine approximations. The generalization allows to compute the fundamental units of the algebraic rings and to find all solutions of a certain class of ...
Bruno A. D. http://library.keldysh.ru/author_page.asp?aid=1428
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Diophantine approximations and Diophantine equations
, 1991 "This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations.
Schmidt, Wolfgang M
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The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
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On a problem in simultaneous diophantine approximation: Littlewood's conjecture
Acta Mathematica, 2000 Littlewood's conjecture that given any real numbers \(\alpha, \beta\), \(\liminf_{q\to \infty}q\|q\alpha \|\|q\beta \|=0\) \((\|\alpha\|= \min\{|x-k|: k\in\mathbb{Z}\})\) has resisted resolution for many years. The conjecture holds if either \(\alpha\) or \(\beta\) are not badly approximable (\(\alpha\) is badly approximable if \(q\|q\alpha\|\geq c ...
Pollington, Andrew D., Velani, Sanju L.
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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Combinatorics on number walls and the P(t)$P(t)$‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 1, January 2026.Abstract In 2004, de Mathan and Teulié stated the p$p$‐adic Littlewood conjecture (p$p$‐LC) in analogy with the classical Littlewood conjecture. Let Fq$\mathbb {F}_q$ be a finite field P(t)$P(t)$ be an irreducible polynomial with coefficients in Fq$\mathbb {F}_q$. This paper deals with the analogue of p$p$‐LC over the ring of formal Laurent series over
Steven Robertson
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, 1996 A theory is presented for simultaneous Diophantine approximation by means of minimal sets of lattice points, defined in a certain sense. We show that successive minima can be used to find best simultaneous Diophantine approximations.
Iven +4 more
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A Linear Diophantine Fuzzy Graph‐Theoretic Approach for Planar Dynamic Traffic Optimization
Applied Computational Intelligence and Soft Computing, Volume 2026, Issue 1, 2026.Dynamic urban traffic signal control systems face uncertainties such as fluctuating vehicle densities, unpredictable incidents, and varying driver behaviors, making precise decision‐making highly challenging. To address these complexities, fuzzy planar graphs have been employed for uncertainty modeling.
Waheed Ahmad Khan +5 more
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