Results 91 to 100 of about 2,483 (259)
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 a conjecture in diophantine approximations, II
Journal of Number Theory, 1991 The author continues his investigations from Part I [Acta Math. Sin. 33, No. 5, 712--717 (1990; Zbl 0716.11030)] on the conjecture \((C_ 2)\). An elementary proof of conjecture \((C_ 2)\) for \(n=4\) is given.
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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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DIOPHANTINE APPROXIMATION FOR ALGEBRAIC POINTS ON CURVES
, 2020 A foundational result in Diophantine approximation is Roth's theorem, which asserts that for a given algebraic number $\alpha$ and $\varepsilon>0$, the inequality $|\alpha-p/q| 0$, we get\[m_{D,S}(P)\leq (N_d(D)+\varepsilon) h_R(P) +O(1)\]for all $P\in C(
Plante, Thomas
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A uniform metrical theorem in multiplicative Diophantine approximation
Forum of Mathematics, SigmaFor Lebesgue generic $({x}_1,x_2)\in \mathbb {R}^2$ , we investigate the distribution of small values of products $q\cdot \|qx_1\| \cdot \|qx_2\|$ with $q\in \mathbb {N}$ , where $\|\cdot \|$ denotes the distance to the closest ...
Michael Björklund +2 more
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Counting algebraic numbers in short intervals with rational points
Журнал Белорусского государственного университета: Математика, информатика, 2019 In 2012 it was proved that real algebraic numbers follow a nonuniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970).
Vasily I. Bernik +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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Weighted simultaneous Diophantine approximation in a variety of settings [PDF]
, 2021 This thesis considers weighted simultaneous Diophantine approximation in a variety of settings, including approximation over real manifolds, p-adic manifolds and p-adic coordinate hyperplanes.
Ward, Benjamin
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Multipoint nonlocal problem for factorized equation with dependent coefficients in conditions
Karpatsʹkì Matematičnì Publìkacìï, 2015 The conditions of correct solvability of multipoint nonlocal problem for factorized PDE with coefficients in conditions, which depends on one real parameter, is established.
P.B. Vasylyshyn, I.Ya. Savka, I.S. Klyus
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Exponents of Diophantine Approximation [PDF]
, 2016 37 pages, comments are welcome!
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