Results 51 to 60 of about 3,571 (122)
Iitaka fibrations and integral points: A family of arbitrarily polarized spherical threefolds
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract Studying Manin's program for a family of spherical log Fano threefolds, we determine the asymptotic number of integral points whose height associated with an arbitrary ample line bundle is bounded. This confirms a recent conjecture by Santens and sheds new light on the logarithmic analog of Iitaka fibrations, which have not yet been adequately
Ulrich Derenthal, Florian Wilsch
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Inhomogeneous Khintchine–Groshev theorem without monotonicity
Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2639-2657, September 2025.Abstract The Khintchine–Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of ψ$\psi$‐approximable numbers, given a monotonic function ψ$\psi$. Allen and Ramírez removed the monotonicity condition from the inhomogeneous Khintchine–Groshev theorem for cases with nm⩾3$nm\geqslant 3$ and ...
Seongmin Kim
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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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A circle method approach to K‐multimagic squares
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract In this paper, we investigate K$K$‐multimagic squares of order N$N$. These are N×N$N \times N$ magic squares that remain magic after raising each element to the k$k$th power for all 2⩽k⩽K$2 \leqslant k \leqslant K$. Given K⩾2$K \geqslant 2$, we consider the problem of establishing the smallest integer N2(K)$N_2(K)$ for which there exist ...
Daniel Flores
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Strong characterizing sequences in simultaneous diophantine approximation
Journal of Number Theory, 2003 In this paper, it is proved that: if \(1,\alpha_1,\dots, \alpha_t\in\mathbb{R}\) are linearly independent over the rationals, there is a subset \(A\subset\mathbb{N}\), \(| A|=\infty\), such that \(\sum_{n\in A}\| n\beta\|\) is finite if and only if \(\beta\in G\), the group generated by \(1,\alpha_1,\dots, \alpha_t\).
Biró, András, T. Sós, Vera
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K‐stable Fano threefolds of rank 2 and degree 28
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract Moduli spaces of Fano varieties have historically been difficult to construct. However, recent work has shown that smooth K‐polystable Fano varieties of fixed dimension and volume can be parametrised by a quasi‐projective moduli space. In this paper, we prove that all smooth Fano threefolds with Picard rank 2 and degree 28 are K‐polystable ...
Joseph Malbon
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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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Simultaneous Diophantine approximation - logarithmic improvements
, 2016 This paper is devoted to the study of a problem of Cassels in multiplicative Diophantine approximation which involves minimising values of a product of affine linear forms computed at integral points. It was previously known that values of this product become arbitrary close to zero, and we establish that, in fact, they approximate zero with an ...
Gorodnik, Alexander, Vishe, Pankaj
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Localized and Extended Phases in Square Moiré Patterns
Annalen der Physik, Volume 537, Issue 6, June 2025.Rotated superimposed lattices in two dimensions, the termed moiré patterns, represent a clear example of how the structure affects the physical properties of a particle moving on it. A robust numerical treatment of continuous and discrete models leads to confirm that while localized states result from angles that produce non‐commensurable lattices ...
C. Madroñero +2 more
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Simultaneous Diophantine Approximation and Asymptotic Formulae on Manifolds
Journal of Number Theory, 1996 Let \(\psi(q) \in \mathbb{N}\) for \(q=1, 2, 3, \dots\) be decreasing such that for some \(k \in \mathbb{N}\) the series \(\sum\psi(q)^k\) is divergent. As a slight variation of Khintchine's theorem on simultaneous diophantine approximation, it is known that, for almost all \((x_1, \dots, x_k) \in\mathbb{R}^k\) there are infinitely many solutions of ...
Dodson, M.M. +2 more
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