Results 41 to 50 of about 476,689 (165)
Formulae for the number of non-negative integer solutions of linear Diophantine equation and inequality [PDF]
, 2023 New formulae are presented for the number $P(b)$ of non-negative integer solutions of a Diophantine equation $\sum_{i=1}^{n}a_ix_i=b$ and for the number $Q(b)$ of non-negative integer solutions of the Diophantine inequality $\sum_{i=1}^{n}a_ix_i\leq b$ $(
Samsonadze, Eteri
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On the exceptional set in Littlewood's discrete conjecture
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
wiley +1 more source
On the diophantine inequality |X^2-cXY^2+Y^4|<=c+2 [PDF]
, 2013 Generalizing some earlier results, we find all the cop- rime integer solutions of the Diophantine inequality |X2 - cXY 2 + Y 4|
Pink, István +7 more
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Double‐jump phase transition for the reverse Littlewood–Offord problem
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Erdős conjectured in 1945 that for any unit vectors v1,…,vn$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
wiley +1 more source
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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Diophantine Inequalities for Polynomial Rings
Journal of Number Theory, 1999 The author studies the Hardy-Littlewood method for the Laurent series field \(\mathbb F_q ((1/T))\) over the finite field \(\mathbb F_q\) with \(q\) elements. He shows that if \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are nonzero elements in \(\mathbb F_q ((1/T))\) satisfying \(\lambda_1/\lambda_2\not\in \mathbb F_q(T)\) and \(\text{sgn} (\lambda_1)+
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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
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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 ...
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The High Cost of Gender Inequality in Earnings
, 2018 This first note in the series on the cost of gender inequality focuses on the losses in national wealth due to gender inequality in earnings. There is a substantial literature on the impact of gender inequality on
de la Brière, Bénédicte +1 more
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