T. Schoen, I. D. Shkredov, “Roth's theorem in many variables”, Israel Journal of Mathematics, 2014, Volume 199, Issue 1, Pages 287

Loading [MathJax]/jax/output/CommonHTML/jax.js

Israel Journal of Mathematics

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	Main page
	About this project
	Software
	Classifications
	Links
	Terms of Use

	Search papers
	Search references

	RSS
	Current issues
	Archive issues
	What is RSS

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Israel Journal of Mathematics, 2014, Volume 199, Issue 1, Pages 287–308
DOI: https://doi.org/10.1007/s11856-013-0049-0 (Mi ijm2)

This article is cited in 11 scientific papers (total in 11 papers)

Roth's theorem in many variables

T. Schoen^a, I. D. Shkredov^bcd

^a Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznán, Poland
^b Division of Algebra and Number Theory, Steklov Mathematical Institute, ul. Gubkina, 8, Moscow, Russia, 119991
^c IITP RAS, Bolshoy Karetny per. 19, Moscow, Russia, 127994
^d Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya str. 14, Yaroslavl, Russia, 150000

Full-text PDF Citations (11)

DOI: https://doi.org/10.1007/s11856-013-0049-0

Abstract: We prove that if

$A\subseteq\{1,\dots,N\}$ has no nontrivial solution to the equation

$x_1 + x_2 + x_3 + x_4 + x_5 = 5y$ , then

$|A|\ll Ne^{-c(\log N)^{1/7}}$ ,

$c> 0$ . In view of the well-known Behrend construction, this estimate is close to best possible.

Funding agency	Grant number
Ministry of Science and Higher Education (Poland)	N201 543538
Russian Foundation for Basic Research	11-01-00759 12-01-33080
Ministry of Education and Science of the Russian Federation	11.G34.31.0053 2519.02012.1
The author is partly supported by MNSW grant N N201 543538. The author is supported by grant RFFI NN 11-01-00759, Russian Government project 11.G34.31.0053, Federal Program “Scientific and scientific–pedagogical staff of innovative Russia” 2009–2013, grant mol a ved 12-01-33080 and grant Leading Scientific Schools N 2519.02012.1.

Received: 25.10.2011
Revised: 30.10.2012

Bibliographic databases:

Document Type: Article

Language: English

Linking options:

https://www.mathnet.ru/eng/ijm2

This publication is cited in the following 11 articles:

Xiumin Ren, Qingqing Zhang, Rui Zhang, “Roth-type theorem for quadratic system in Piatetski-Shapiro primes”, Journal of Number Theory, 257 (2024), 1
Tomasz Schoen, “Translation-Invariant Equations With at Least Four Variables”, International Mathematics Research Notices, 2024
Thomas F. Bloom, Olof Sisask, “The Kelley–Meka bounds for sets free of three-term arithmetic progressions”, Ess. Number Th., 2:1 (2023), 15
Tomasz Schoen, “Improved bound in Roth's theorem on arithmetic progressions”, Advances in Mathematics, 386 (2021), 107801
Stephen R. Chestnut, Robert Hildebrand, Rico Zenklusen, “Sublinear Bounds for a Quantitative Doignon–Bell–Scarf Theorem”, SIAM J. Discrete Math., 32:1 (2018), 352
Joshua Grochow, “New applications of the polynomial method: The cap set conjecture and beyond”, Bull. Amer. Math. Soc., 56:1 (2018), 29
Karol Cwalina, Tomasz Schoen, “Tight bounds on additive Ramsey-type numbers”, J. London Math. Soc., 96:3 (2017), 601
TOMASZ SCHOEN, OLOF SISASK, “ROTH'S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS”, Forum of Mathematics, Sigma, 4 (2016)
Pierre Fraigniaud, Ivan Rapaport, Ville Salo, Ioan Todinca, Lecture Notes in Computer Science, 9888, Distributed Computing, 2016, 342
J. Wolf, “Finite field models in arithmetic combinatorics – ten years on”, Finite Fields and Their Applications, 32 (2015), 233
I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	184

Что такое QR-код?

Registration to the website

Logotypes