Results 41 to 50 of about 370,794 (154)

On a class of diophantine inequalities [PDF]

Bulletin of the Australian Mathematical Society, 1973
As a special case of more general results, it is proved in this note that, if α is any real number and δ any positive number, then there exists a positive integer X such that the inequalityhas infinitely many solutions in positive integers h and Yh.The method depends on the study of infinite sequences of real linear forms in a fixed number of variables.
openaire   +1 more source

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

On two inequalities for the composition of arithmetic functions [PDF]

, 2012
A paper about two inequalities for the composition of arithmetic ...
József Sándor, Sandor, Jozsef
core   +1 more source

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, Julien Portier, Victor Souza   +2 more
wiley   +1 more source

Sums of three positive cubes

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
wiley   +1 more source

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, Carl‐Fredrik Nyberg‐Brodda   +1 more
wiley   +1 more source

On Diophantine transference principles [PDF]

, 2018
We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for inhomogeneous Diophantine exponents of affine subspaces and their ...
ANTOINE MARNAT, Ghosh, Anish, ANISH GHOSH, Marnat, Antoine   +3 more
core   +1 more source

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

Integral zeroes of Krawtchouk polynomials [PDF]

, 2012
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.Krawtchouk polynomials appear in many various areas of mathematics starting from discrete mathematics (e.g., in coding theory), association schemes, and in ...
Alenezi, Ahmad M
core   +4 more sources

Gowers norms control diophantine inequalities [PDF]

Algebra & Number Theory, 2017
A central tool in the study of systems of linear equations with integer coefficients is the Generalised von Neumann Theorem of Green and Tao. This theorem reduces the task of counting the weighted solutions of these equations to that of counting the weighted solutions for a particular family of forms, the Gowers norms $\Vert f \Vert_{U^{s+1}[N]}$ of ...
openaire   +4 more sources