Rado's criterion over squares and higher powers

DOI10.4171/JEMS/1047zbMath1497.11028arXiv1806.05002OpenAlexW3132786080MaRDI QIDQ2031686

Sean Prendiville, Sam Chow, Sofia Lindqvist

Publication date: 10 June 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05002

zbMATH Keywords

smooth numbers arithmetic combinatorics arithmetic Ramsey theory restriction theory

Mathematics Subject Classification ID

Diophantine equations in many variables (11D72) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (6)

Analytic number theory. Abstracts from the workshop held November 6--12, 2022 ⋮ Towards characterizing the 2-Ramsey equations of the form \(ax + by = p(z)\) ⋮ Unnamed Item ⋮ On sumsets of subsets of squares ⋮ A Diophantine Ramsey theorem ⋮ Translation invariant quadratic forms and dense sets of primes

Cites Work

Unnamed Item
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Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
Partition regularity and the primes
On \(\Lambda\) (p)-subsets of squares
A Schur-type addition theorem for primes
Roth's theorem in the primes
Linear equations in primes
Quantitative theorems for regular systems of equations
A new iterative method in Waring's problem
On partition regular systems of equations
Large improvements in Waring's problem
Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
Supersaturation in posets and applications involving the container method
Ramsey properties of nonlinear Diophantine equations
Studien zur Kombinatorik
On arithmetic structures in dense sets of integers
Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour
On the interplay between additive and multiplicative largeness and its combinatorial applications
Monochromatic sums and products in \(\mathbb{N}\)
Density and Ramsey type results on algebraic equations with restricted solution sets
Partitionen und lineare Gleichungssysteme
Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer
Monochromatic sums and products
Higher order Fourier analysis of multiplicative functions and applications
Weyl sums, mean value estimates, and Waring's problem with friable numbers
The Asymptotic Formula in Waring’s Problem
ON A DIAGONAL QUADRIC IN DENSE VARIABLES
An arithmetic regularity lemma, associated counting lemma, and applications
Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers
On Certain Sets of Positive Density
Forms in many variables
On the Number of Monochromatic Solutions of x + y =z 2
WARING'S PROBLEM WITH SHIFTS
On Waring's Problem: Some Refinements
Partitions and Sums and Products of Integers
Combinatorial Proofs of the Polynomial van der Waerden Theorem and the Polynomial Hales-Jewett Theorem
Tight bounds on additive Ramsey-type numbers
A Transference Approach to a Roth-Type Theorem in the Squares
Roth–Waring–Goldbach
Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case
Monochromatic solutions to x+y=z2 in the interval [N,cN4]
Partition regularity and multiplicatively syndetic sets
On Translation Invariant Quadratic Forms in Dense Sets
Four variants of the Fourier-analytic transference principle
Monochromatic Solutions to
Simultaneous Quadratic Equations
Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
ON THE DISTRIBUTION OF THE SEQUENCE n2 (mod 1)
On Certain Sets of Integers
On Waring's problem for cubes.

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