Results 31 to 40 of about 304 (165)
Symmetric modular Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 2006 In this paper we study and characterize those Diophantine inequalities a x mod
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Counting intrinsic Diophantine approximations in simple algebraic groups
, 2022 We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple algebraic groups, at arbitrarily small ...
Nevo, Amos +2 more
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One Cubic Diophantine Inequality [PDF]
Journal of the London Mathematical Society, 2000 Let \(F(x)\) be a cubic form with real coefficients in \(s\) variables. \textit{J. Pitman} [J. Lond. Math. Soc. 43, 119-126 (1968; Zbl 0164.05301)] proved that there exists \(s_0> 0\) such that for any \(s\geq s_0\) the inequality \[ |F(x)|< 1 \tag{1} \] is solvable in \({\mathbf x}\in \mathbb{Z}^3\setminus \{\mathbf{0}\}\). About the quantitative part,
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On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
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ALGORITHMS FOR SOLVING THE SYSTEMS OF LINEAR CONSTRAINTS WITH INTEGER COEFFICIENTS IN THE SET {0, 1}
Міжнародний науково-технічний журнал "Проблеми керування та інформатики"The basic concepts of linear homogeneous and inhomogeneous equations and inequalities in the domain {0, 1}, are considered the properties of the TSS-algorithm, which may be applied in solving those systems are described.
С.Л. Кривий +1 more
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Multiplicatively dependent integer vectors on a hyperplane
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman +2 more
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Vinogradov's mean value theorem via efficient congruencing [PDF]
, 2012 We obtain estimates for Vinogradov's integral that for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided.
Wooley, Trevor D., Trevor D. Wooley
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Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
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On transfer inequalities in Diophantine approximation, II [PDF]
Mathematische Zeitschrift, 2009 We refine Khintchine Transference Principle which relates the measure of simultaneous rational approximation of an $n$ real numbers with the measure of linear independence of these $n$ numbers. Khintchine's inequalities are known to be optimal. However, they may be sharpened by taking into account two further uniform exponents.
Bugeaud, Yann, Laurent, Michel
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New results on embeddings of self‐similar sets via renormalization
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
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