Results 31 to 40 of about 9,377,044 (73)
Discretised sum‐product theorems by Shannon‐type inequalities
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract By making use of arithmetic information inequalities, we give a strong quantitative bound for the discretised ring theorem. In particular, we show that if A⊂[1,2]$A \subset [1,2]$ is a (δ,σ)$(\delta,\sigma)$‐set, with |A|=δ−σ$|A| = \delta ^{-\sigma }$, then A+A$A+A$ or AA$AA$ has δ$\delta$‐covering number at least δ−c|A|$\delta ^{-c}|A|$ for ...
András Máthé, William O'Regan
wiley +1 more source
The structure of sets with cube‐avoiding sumsets
Mathematika, Volume 71, Issue 4, October 2025.Abstract Suppose G$G$ is a finite abelian group, Z0⊂G$Z_0 \subset G$ is not contained in any strict coset in G$G$, and E,F$E,F$ are dense subsets of Gn$G^n$ such that the sumset E+F$E+F$ avoids Z0n$Z_0^n$. We show that E$E$ and F$F$ are almost entirely contained in sets defined by a bounded number of coordinates, that is, sets E′×GIc$E^{\prime } \times
Thomas Karam, Peter Keevash
wiley +1 more source
Characterizing the sum of two cubes [PDF]
, 2003 An intrinsic characterization of positive integers which can be represented as the sum or difference of two cubes is given. Every integer has a smallest multiple with is a sum of two cubes and such that the multiple, in the form of an iterated function ...
Kevin A. Broughan, Broughan, Kevin A.
core +1 more source
Strong External Difference Families and Classification of α‐Valuations
Journal of Combinatorial Designs, Volume 33, Issue 9, Page 343-356, September 2025.ABSTRACT One method of constructing ( a 2 + 1 , 2 , a , 1 )‐SEDFs (i.e., strong external difference families) in Z a 2 + 1 makes use of α‐valuations of complete bipartite graphs K a , a. We explore this approach and we provide a classification theorem which shows that all such α‐valuations can be constructed recursively via a sequence of “blow‐up ...
Donald L. Kreher +2 more
wiley +1 more source
Infinite unrestricted sumsets of the form B+B$B+B$ in sets with large density
Bulletin of the London Mathematical Society, Volume 57, Issue 1, Page 48-68, January 2025.Abstract For a set A⊂N$A \subset {\mathbb {N}}$, we characterize the existence of an infinite set B⊂N$B \subset {\mathbb {N}}$ and t∈{0,1}$t \in \lbrace 0,1\rbrace$ such that B+B⊂A−t$B+B \subset A-t$, where B+B={b1+b2:b1,b2∈B}$B+B =\lbrace b_1+b_2\colon b_1,b_2 \in B\rbrace$, in terms of the density of the set A$A$. Specifically, when the lower density
Ioannis Kousek, Tristán Radić
wiley +1 more source
The structure and density of k$k$‐product‐free sets in the free semigroup and group
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract The free semigroup F$\mathcal {F}$ on a finite alphabet A$\mathcal {A}$ is the set of all finite words with letters from A$\mathcal {A}$ equipped with the operation of concatenation. A subset S$S$ of F$\mathcal {F}$ is k$k$‐product‐free if no element of S$S$ can be obtained by concatenating k$k$ words from S$S$, and strongly k$k$‐product‐free ...
Freddie Illingworth +2 more
wiley +1 more source
Brauer–Manin obstructions requiring arbitrarily many Brauer classes
Bulletin of the London Mathematical Society, Volume 56, Issue 5, Page 1587-1604, May 2024.Abstract On a projective variety defined over a global field, any Brauer–Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show that this subgroup can require arbitrarily many generators.
Jennifer Berg +6 more
wiley +1 more source
Additive and geometric transversality of fractal sets in the integers
Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.Abstract By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we introduce and study — in the discrete context of the integers — analogs of some of the ...
Daniel Glasscock +2 more
wiley +1 more source
Numerical Linear Algebra with Applications, Volume 31, Issue 1, January 2024.Abstract Fully implicit Runge–Kutta methods offer the possibility to use high order accurate time discretization to match space discretization accuracy, an issue of significant importance for many large scale problems of current interest, where we may have fine space resolution with many millions of spatial degrees of freedom and long time intervals ...
Owe Axelsson +2 more
wiley +1 more source
Large sums of high‐order characters
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract Let χ$\chi$ be a primitive character modulo a prime q$q$, and let δ>0$\delta > 0$. It has previously been observed that if χ$\chi$ has large order d⩾d0(δ)$d \geqslant d_0(\delta)$ then χ(n)≠1$\chi (n) \ne 1$ for some n⩽qδ$n \leqslant q^{\delta}$, in analogy with Vinogradov's conjecture on quadratic non‐residues.
Alexander P. Mangerel
wiley +1 more source