Roth-Waring-Goldbach

被引：22
作者：
Chow, Sam [1 ]
机构：
[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2018年 / 2018卷 / 08期
基金：
英国工程与自然科学研究理事会;
关键词：
REPRESENTATION; EQUATIONS; THEOREM; NUMBERS;
D O I：
10.1093/imrn/rnw307
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We use Green's transference principle to show that any subset of the dth powers of primes with positive relative density contains nontrivial solutions to a translation-invariant linear equation in d(2) + 1 or more variables, with explicit quantitative bounds.
引用
收藏
页码：2341 / 2374
页数：34
相关论文
共 37 条
[1]  
[Anonymous], ARXIV150909200
[2]  
[Anonymous], [No title captured]
[3]  
Apostol T., 1976, UNDERGRADUATE TEXTS
[4]  
Baker RC, 1986, LONDON MATH SOC MONO, V1
[5]   Estimates for representation numbers of quadratic forms [J].
Blomer, Valentin ;
Granville, Andrew .
DUKE MATHEMATICAL JOURNAL, 2006, 135 (02) :261-302
[6]   A quantitative improvement for Roth's theorem on arithmetic progressions [J].
Bloom, T. F. .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 93 :643-663
[7]   Translation invariant equations and the method of Sanders [J].
Bloom, Thomas F. .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2012, 44 :1050-1067
[8]   ON LAMBDA-L (P)-SUBSETS OF SQUARES [J].
BOURGAIN, J .
ISRAEL JOURNAL OF MATHEMATICS, 1989, 67 (03) :291-311
[9]  
Bourgain J., 1993, Geom. Funct. Anal., V3, P107
[10]  
Bourgain J, 2016, ARXIV160108173
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