發佈時間：2013-05-27
An exciting paper about gaps between prime numbers - a step closer to proving the twin prime conjecture. Extra footage at http://youtu.be/D4_sNKoO-RA
The proof was published by Yitang "Tom" Zhang from the University of New Hampshire.
We're discussing it in simple terms with Numberphile regulars - physicists Ed Copeland and Tony Padilla from the University of Nottingham.
Brown papers from this video available: http://bit.ly/brownpapers
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Google Plus: http://bit.ly/numberGplus
Tumblr: http://numberphile.tumblr.com
Videos by Brady Haran
Brady's other channels include:
Chemistry stuff
Physics and astronomy
Computer stuff
Numbers and maths
Space stuff
Science and behind the scenes
Food science
Big science facilities
Favourite scientists
Academic look at the Bible
Modern language and culture
Philosophy stuff
Psychology stuff
類別
科學與技術
授權
標準 YouTube 授權
Bounded gaps betweenprimes
YitangZhang
Abstract
It is proved that lim inf n→∞ (pn+1−pn)<7× 107,
where pn is the n-th prime.
OurmethodisarefinementoftherecentworkofGoldston,PintzandYildirimonthesmallgapsbetweenconsecutiveprimes.AmajoringredientoftheproofisastrongerversionoftheBombieri-Vinogradovtheoremthatisapplicablewhenthemoduliarefreefromlargeprimedivisorsonly(seeTheorem2below),butitisadequateforourpurpose. Contents 1.Introduction 22.Notationandsketchoftheproof33.Lemmas 74.UpperboundforS1165.LowerboundforS2 226.Combinatorialarguments247.Thedispersionmethod278.EvaluationofS3(r,a)299.EvaluationofS2(r,a) 3010.AtruncationofthesumofS1(r,a) 3411.EstimationofR1(r,a;k):TheTypeIcase3912.EstimationofR1(r,a;k):TheTypeIIcase4213.TheTypeIIIestimate:Initialste
http://wenku.baidu.com/view/a93e31ca50e2524de5187e34.html
※ 編輯: ott 時間: 2013-06-26 12:16:55
※ 同主題文章:
● 06-26 03:48 □ Gaps between Primes - Numberphile
03-25 02:21 Re Gaps between Primes - Numberphile
※ 看板: ott 文章推薦值: 0 目前人氣: 0 累積人氣: 204
回列表(←)
分享