The three primes theorem with almost equal summands

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Baker R. C. and Harman G. 1998The three primes theorem with almost equal summandsPhil. Trans. R. Soc. A.356763–780http://doi.org/10.1098/rsta.1998.0184SectionRestricted accessThe three primes theorem with almost equal summands R. C. Baker R. C. Baker Department of Mathematics, Brigham Young University, Provo, UT 84602, USA Google Scholar Find this author on PubMed Search for more papers by this author and G. Harman G. Harman Department of Mathematics, Brigham Young University, Provo, UT 84602, USA Google Scholar Find this author on PubMed Search for more papers by this author R. C. Baker R. C. Baker Department of Mathematics, Brigham Young University, Provo, UT 84602, USA Google Scholar Find this author on PubMed Search for more papers by this author and G. Harman G. Harman Department of Mathematics, Brigham Young University, Provo, UT 84602, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:15 March 1998https://doi.org/10.1098/rsta.1998.0184AbstractThe problem of representing all sufficiently large odd numbers as the sum of three nearly equal primes is tackled using the Hardy–Littlewood circle method in tandem with a sieve method. A combination of the Harman and vector sieves, as developed by Baker, Harman and Pintz, is used. To do this, the major arcs of the circle method involve the investigation of the mean–values of Dirichlet polynomials, while the minor arcs demand short–range estimates for exponential sums. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Matomäki K, Maynard J and Shao X (2017) Vinogradov's theorem with almost equal summands, Proceedings of the London Mathematical Society, 10.1112/plms.12040, 115:2, (323-347), Online publication date: 1-Aug-2017. Harman G (2016) PRIMES IN BEATTY SEQUENCES IN SHORT INTERVALS, Mathematika, 10.1112/S0025579315000376, 62:2, (572-586), Online publication date: 1-Jan-2016. Shiu P (2016) Pseudoperfect numbers with no small prime divisors, The Mathematical Gazette, 10.1017/S0025557200185146, 93:528, (404-409), Online publication date: 1-Nov-2009. Lü G (2006) Hua’s Theorem on Five Almost Equal Prime Squares, Acta Mathematica Sinica, English Series, 10.1007/s10114-005-0750-y, 22:3, (907-916), Online publication date: 1-May-2006. Guy R (2004) Additive Number Theory Unsolved Problems in Number Theory, 10.1007/978-0-387-26677-0_4, (159-208), . Pan C (2002) A Historical Comment about the GVT in Short Interval Number Theoretic Methods, 10.1007/978-1-4757-3675-5_18, (351-367), . This Issue15 March 1998Volume 356Issue 1738Theme Issue ‘Applications of the Hardy–Littlewood method’ compiled by R. C. Vaughan and T. D. Wooley Article InformationDOI:https://doi.org/10.1098/rsta.1998.0184Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/03/1998Published in print15/03/1998 License: Citations and impact KeywordsDirichlet polynomialssieve methodsexponential sumsHardy–Littlewood circle methoddistribution of primesGoldbach–Vinogradov theorem