On Roth's theorem on progressions
From MaRDI portal
Publication:640798
DOI10.4007/annals.2011.174.1.20zbMath1264.11004arXiv1011.0104OpenAlexW3100139723WikidataQ55966507 ScholiaQ55966507MaRDI QIDQ640798
Publication date: 20 October 2011
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1011.0104
Fourier analysisRoth's theoremarithmetic progressionsBohr setsbourgainisationCroot-SisaskKatz-Koesterthree-term progressions
Related Items (64)
Logarithmic bounds for Roth's theorem via almost-periodicity ⋮ Additive combinatorics and graph theory ⋮ Generalizations of Fourier analysis, and how to apply them ⋮ Some Properties of Lower Level-Sets of Convolutions ⋮ The equidistant dimension of graphs ⋮ Ramsey-type numbers involving graphs and hypergraphs with large girth ⋮ On the classification of Stanley sequences ⋮ Short proofs of some extremal results. II. ⋮ On linear configurations in subsets of compact abelian groups, and invariant measurable hypergraphs ⋮ A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1. ⋮ ON A DIAGONAL QUADRIC IN DENSE VARIABLES ⋮ New applications of the polynomial method: The cap set conjecture and beyond ⋮ Improved bounds on the dimensions of sets that avoid approximate arithmetic progressions ⋮ An application of the sum-product phenomenon to sets avoiding several linear equations ⋮ Van der Waerden function and colorings of hypergraphs with large girth ⋮ Covering the Large Spectrum and Generalized Riesz Products ⋮ A generalization of Roth's theorem in function fields ⋮ A new lower bound for van der Waerden numbers ⋮ Arithmetic progressions in multiplicative groups of finite fields ⋮ Tower-type bounds for Roth's theorem with popular differences ⋮ Higher moments of convolutions ⋮ Novel structures in Stanley sequences ⋮ Long arithmetic progressions in \(A+A+A\) with \(A\) a prime subset ⋮ Roth's theorem and the Hardy-Littlewood majorant problem for thin subsets of primes ⋮ Quantitative structure of stable sets in finite abelian groups ⋮ The Kelley-Meka bounds for sets free of three-term arithmetic progressions ⋮ Roth-type theorem for quadratic system in Piatetski-Shapiro primes ⋮ Maximal sets with no solution to \(x+y=3z\) ⋮ NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR ⋮ On Systems of Complexity One in the Primes ⋮ Ramsey-type numbers involving graphs and hypergraphs with large girth ⋮ Unnamed Item ⋮ Embedding Graphs into Larger Graphs: Results, Methods, and Problems ⋮ The NOF multiparty communication complexity of composed functions ⋮ Colourings of Uniform Hypergraphs with Large Girth and Applications ⋮ Enumerating solution-free sets in the integers ⋮ Progression-free sets in \(\mathbb{Z}_4^n\) are exponentially small ⋮ An arithmetic transference proof of a relative Szemerédi theorem ⋮ On the complexity of finding and counting solution-free sets of integers ⋮ An improved lower bound related to the Furstenberg-Sárközy theorem ⋮ Exploiting word-level parallelism for fast convolutions and their applications in approximate string matching ⋮ Caps and progression-free sets in \(\mathbb{Z}_m^n\) ⋮ Nil Bohr\(_0\)-sets and polynomial recurrence ⋮ MATRIX PROGRESSIONS IN MULTIDIMENSIONAL SETS OF INTEGERS ⋮ ON IMPROVING ROTH'S THEOREM IN THE PRIMES ⋮ Roth's theorem in many variables ⋮ ADDITIVE DIMENSION AND A THEOREM OF SANDERS ⋮ A subexponential upper bound for van der Waerden numbers \(W(3,k)\) ⋮ ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS ⋮ Some remarks on barycentric-sum problems over cyclic groups ⋮ Finite field models in arithmetic combinatorics -- ten years on ⋮ Improved bound in Roth's theorem on arithmetic progressions ⋮ A Prime Analogue of Roth’s Theorem in Function Fields ⋮ ARITHMETIC PROGRESSIONS IN SETS OF SMALL DOUBLING ⋮ Arithmetic progressions, different regularity lemmas and removal lemmas ⋮ A short remark on the multiplicative energy of the spectrum ⋮ On sets with small sumset and m-sum-free sets in Z/pZ ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ A Roth-type theorem with mixed powers ⋮ On sets of integers which contain no three terms in geometric progression ⋮ MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS ⋮ Large sets avoiding linear patterns ⋮ On the growth of Stanley sequences ⋮ New bounds on cap sets
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On certain other sets of integers
- Near optimal bounds in Freiman's theorem
- A probabilistic technique for finding almost-periods of convolutions
- Roth's theorem in the primes
- Roth's theorem on progressions revisited
- An improved construction of progression-free sets
- A polynomial bound in Freiman's theorem.
- On subsets of finite Abelian groups with no 3-term arithmetic progressions
- A linear bound on the dimension in Green-Ruzsa's theorem
- On triples in arithmetic progression
- Integer sets containing no arithmetic progressions
- ADDITIVE PROPERTIES OF MULTIPLICATIVE SUBGROUPS OF Fp
- A Note on Elkin’s Improvement of Behrend’s Construction
- On Additive Doubling and Energy
- Integer Sets Containing No Arithmetic Progressions
- On Certain Sets of Integers
- On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
- On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
- The true complexity of a system of linear equations
- On the best constant in Marcinkiewicz-Zygmund inequality
This page was built for publication: On Roth's theorem on progressions