Results 21 to 30 of about 114 (107)
Kripke on Gödel Incompleteness
Theoria, Volume 92, Issue 3, June 2026.ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
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Simultaneous Diophantine approximation of rationals by rationals
Journal of Number Theory, 1986 For positive integers \(n\geq 2\), \(B\geq 2\), let \(S_ n(B)\) denote the set of rational vectors \(\alpha =(a_ 1/B,...,a_ n/B)\) with \(a_ j\in {\mathbb{Z}}\), \(0\leq a_ j0\), define N(\(\alpha\),\(\Delta)\) as the number of vectors \(\zeta =(x_ 1/x,...,x_ n/x)\) with \(1\leq ...
Lagarias, Jeffrey C, Hastad, Johan T
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Simultaneous diophantine approximation with square-free numbers [PDF]
Acta Arithmetica, 1993 A set \(\alpha_ 1,\dots,\alpha_ s\) of real numbers is said to be weakly compatible if \(\sum_{j=1}^ s \ell_ j \alpha_ j=u/v\) with \((u,v)=1\) implies that \(v\) is square-free. This condition is necessary and sufficient for \[ \liminf_{\mu^ 2(n)=1} \max_ j\|\alpha_ j n\|=0, \] where \(\|\cdot\|\) denotes the fractional part, as usual.
Baker, Roger C. +2 more
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Generalized free wreath products and their operator algebras
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
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Double‐jump phase transition for the reverse Littlewood–Offord problem
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Erdős conjectured in 1945 that for any unit vectors v1,…,vn$v_1, \ldots, v_n$ in R2$\mathbb {R}^2$ and signs ε1,…,εn$\varepsilon _1, \ldots, \varepsilon _n$ taken independently and uniformly in {−1,1}$\lbrace -1,1\rbrace$, the random Rademacher sum σ=ε1v1+⋯+εnvn$\sigma = \varepsilon _1 v_1 + \cdots + \varepsilon _n v_n$ satisfies ∥σ∥2⩽1$\Vert \
Lawrence Hollom +2 more
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Simultaneous diophantine approximation of rational numbers [PDF]
Acta Arithmetica, 1972 For any real number \(x\), let \(\Vert x\Vert\) denote the distance from \(x\) to the nearest integer. Let \(n\) be any positive integer and let \(\sigma = (s_1, \ldots, s_n)\) denote an arbitrary point in the set \(S^n\) of \(n\)-dimensional points all of whose coordinates are rational noninteger numbers.
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Successive Minima and Best Simultaneous Diophantine Approximations [PDF]
Monatshefte für Mathematik, 2005 We study the problem of best approximations of a vector $α\in{\mathbb R}^n$ by rational vectors of a lattice $Λ\subset {\mathbb R}^n$ whose common denominator is bounded. To this end we introduce successive minima for a periodic lattice structure and extend some classical results from geometry of numbers to this structure.
Aliev, Iskander, Henk, Martin
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Random Diophantine equations in the primes II
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
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A note on simultaneous diophantine approximation
Manuscripta Mathematica, 1981 Refining earlier investigations due to J.M.MACK [7] by a method of MORDELL it is proved that for any two irrational numbers α, β there exist infinitely many pairs of fractions p/r, q/r satisfying the inequalities $$|\alpha - \frac{p}{r}|< \frac{8}{{13}}r^{ - 3/2} ,|\beta - \frac{q}{r}|< \frac{8}{{13}}r^{ - 3/2} .$$ .
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GCD inequalities arising from codimension‐2 blowups
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Assuming a deep Diophantine geometry conjecture by Vojta, Silverman proved an inequality giving an upper bound for the greatest common divisor (GCD). In this paper, we unconditionally prove a weaker version of this inequality. The main ingredient is the Ru–Vojta theory, which provides an efficient method of using Schmidt subspace theorem.
Yu Yasufuku
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