Results 41 to 50 of about 3,571 (122)
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
wiley +1 more source
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
wiley +1 more source
On inhomogeneous Diophantine approximation and Hausdorff dimension
, 2011 Let $\Gamma = Z A +Z^n$ be a dense subgroup with rank $n+1$ in $R^n$ and let $\omega(A)$ denote the exponent of uniform simultaneous rational approximation to the point $A$.
Laurent, Michel
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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
wiley +1 more source
Generic Nekhoroshev theory without small divisors [PDF]
, 2009 In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P.
Bounemoura, Abed, Niederman, Laurent
core
, 2012 Let Q be an infinite set of positive integers. Denote by W_{\tau, n}(Q) (resp. W_{\tau, n}) the set of points in dimension n simultaneously \tau--approximable by infinitely many rationals with denominators in Q (resp. in N*).
Adiceam, Faustin
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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
wiley +1 more source
Simultaneous diophantine approximation in non-degenerate p-adic manifolds [PDF]
Israel Journal of Mathematics, 2011 S-arithmetic Khintchine-type theorem for products of non-degenerate analytic p-adic manifolds is proved for the convergence case. In the p-adic case the divergence part is also obtained.
Mohammadi, A., Salehi Golsefidy, A.
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Curves of best approximation on wonderful varieties
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3941-3948, December 2025.Abstract We give an unconditional proof of the Coba conjecture for wonderful compactifications of adjoint type for semisimple Lie groups of type An$A_n$. We also give a proof of a slightly weaker conjecture for wonderful compactifications of adjoint type for arbitrary Lie groups.
Christopher Manon +2 more
wiley +1 more source
Metric considerations concerning the mixed Littlewood Conjecture [PDF]
, 2009 The main goal of this note is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan-Teulie Conjecture, also known as the `Mixed Littlewood Conjecture'. Let p be a prime.
Bugeaud, Yann +2 more
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