Results 21 to 30 of about 93 (44)
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
Arbeitsgemeinschaft: Ergodic Theory and Combinatorial Number Theory [PDF]
, 2012 The aim of this Arbeitsgemeinschaft was to introduce young researchers with various backgrounds to the multifaceted and mutually perpetuating connections between ergodic theory, topological dynamics, combinatorics, and number ...
core +2 more sources
A new shift operator-based polynomial method in additive combinatorics
, 2023 We introduce a new form of the polynomial method based on what we call "shift operators," which we use to give efficient and intuitive new proofs of results previously shown using a wide range of polynomial methods, including Alon's Combinatorial ...
Luo, Sammy
core
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
Exact Inference Algorithms and Their Optimization in Bayesian Clustering [PDF]
, 2015 Clustering is a central task in computational statistics. Its aim is to divide observed data into groups of items, based on the similarity of their features.
Kohonen, Jukka
core
A solution to the Erdős-Sárközy-Sós problem on asymptotic Sidon bases of order 3 [PDF]
, 2023 A set $S\subset \mathbb{N}$ is a Sidon set if all pairwise sums $s_1+s_2$ (for $s_1, s_2\in S$, $s_1\leq s_2$) are distinct. A set $S\subset \mathbb{N}$ is an asymptotic basis of order 3 if every sufficiently large integer $n$ can be written as the ...
Pilatte, Cédric
core
Improved stability for the size and structure of iterated sumsets in \(\mathbb{Z}^d\) [PDF]
Let \(A \subset \mathbb{Z}^d\) be a finite set. It is known that the sumset \(NA\) has predictable size (\(\vert NA\vert = P_A(N)\) for some \(P_A(X) \in \mathbb{Q}[X]\)) and structure (all of the lattice points in some finite cone other than all of the ...
Granville, Andrew +2 more
core +1 more source