Results 61 to 70 of about 12,497 (156)
Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
Diophantine Inequalities for Polynomial Rings
Journal of Number Theory, 1999 The author studies the Hardy-Littlewood method for the Laurent series field \(\mathbb F_q ((1/T))\) over the finite field \(\mathbb F_q\) with \(q\) elements. He shows that if \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are nonzero elements in \(\mathbb F_q ((1/T))\) satisfying \(\lambda_1/\lambda_2\not\in \mathbb F_q(T)\) and \(\text{sgn} (\lambda_1)+
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A universal example for quantitative semi‐uniform stability
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora +3 more
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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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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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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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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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Additive Diophantine inequalities with mixed powers II
Mathematika, 1987 Let \(1\leq k_ 1\leq k_ 2...\leq k_ s\) be integers. The author considers the following, so-called inequality problem for \(k_ 1,...,k_ s:\) is it true, that for every s-tuple of non-zero real numbers \((\lambda_ 1,...,\lambda_ s)\) such that at least one quotient \(\lambda_ i/\lambda_ j\) is irrational, the values assumed by \(\sum^{s}_{i=1}\lambda_ ...
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Euclidean algorithms are Gaussian over imaginary quadratic fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We prove that the distribution of the number of steps of the Euclidean algorithm of rationals in imaginary quadratic fields with denominators bounded by N$N$ is asymptotically Gaussian as N$N$ goes to infinity, extending a result by Baladi and Vallée for the real case.
Dohyeong Kim, Jungwon Lee, Seonhee Lim
wiley +1 more source