RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
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 J. Math., 2014, Volume 199, Issue 1, Pages 287–308 (Mi ijm2)  

Roth's theorem in many variables

T. Schoena, I. D. Shkredovbcd

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

Abstract: We prove that if $A\subseteq\{1,…,N\}$ 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.


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

Full text: https:/.../10.1007%2Fs11856-013-0049-0

Bibliographic databases:

Document Type: Article
Received: 25.10.2011
Revised: 30.10.2012
Language: English

Linking options:
  • http://mi.mathnet.ru/eng/ijm2

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:41

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019