Results 81 to 90 of about 11,736 (207)
On the exceptional set in Littlewood's discrete conjecture
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
wiley +1 more source
The Solution of a Diophantine Equation [PDF]
Proceedings of the American Mathematical Society, 1952 in which we suppose that f(y) =f(yi, * ya) is a homogeneous polynomial, with integral coefficients, of degree m, where m is of the form 2P(2q+1), q being a non-negative integer, p is one of the integers 0, 1, * * *, n -1, and thus m 0 0 (mod 2n). We suppose further that the rank of the matrix of the forms Enl aajx (i= 1, , 2n) is 2n -1 and thus we may ...
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Matrix Diophantine equations over quadratic rings and their solutions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The method for solving the matrix Diophantine equations over quadratic rings is developed. On the basic of the standard form of matrices over quadratic rings with respect to $(z,k)$-equivalence previously established by the authors, the matrix ...
N.B. Ladzoryshyn +2 more
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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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Diophantine approximation and filtrations
, 2017 In this talk, I will introduce the notion of height, and how Diophantine inequalities help in Diophantine geometry. Specifically, I'll discuss the theorem of Faltings-Wuestholz and how it uses filtrations to derive Diophantine inequalities.Non ...
McKinnon, David
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IEEE AccessThe Objectives of this study is to extend the concept of q-rung linear Diophantine fuzzy sets (q-RLDFSs), followed by the Near-Earth Asteroids (NEAs) deflection detector.
Maria Shams +4 more
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Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
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HNN extensions and embedding theorems for groups
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract The Higman–Neumann–Neumann (HNN) paper of 1949 is a landmark of group theory in the 20th century. The proof of its main theorem covers less than a page and uses only pre‐existing technology, but the construction that it introduced, the HNN extension, quickly became one of the principal tools of combinatorial group theory, widely used to build ...
Martin R. Bridson +1 more
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Adjugates of Diophantine Quadruples [PDF]
Integers, 2010 AbstractDiophantine
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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
wiley +1 more source