Results 71 to 80 of about 11,736 (207)
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
wiley +1 more source
Restricted simultaneous Diophantine approximation
, 2017 We study the problem of Diophantine approximation on lines in Rd under certain primality ...
Ghosh, Anish, Baier, Stephan
core +1 more source
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
wiley +1 more source
Diophantine Equation in Logarithms [PDF]
, 2023 The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
core
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
wiley +1 more source
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
wiley +1 more source
Advances in Mechanical Engineering, 2023 Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets.
Mudassir Shams +3 more
doaj +1 more source
Moderate Deviation Principles for Lacunary Trigonometric Sums
Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley +1 more source
Systems of Diophantine Equations [PDF]
Proceedings of the American Mathematical Society, 1951 where fi and gi are homogeneous polynomials with integral coefficients, fi being of degree n and gi being of degree m. If there are no integers s> 1, a k, 3' such that ak = sla , ij = s, where X, g are positive integers such that Xn =,m, then Xk= ak, yij=gi3 is defined to be a primitive solution of (1). If Xk=aQk, yij=fi3 is a primitive solution of (1),
openaire +1 more source
Metric Diophantine approximation on homogeneous varieties [PDF]
, 2014 We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish simultaneous Diophantine
Nevo, Amos +3 more
core +1 more source