由买买提看人间百态

boards

本页内容为未名空间相应帖子的节选和存档,一周内的贴子最多显示50字,超过一周显示500字 访问原贴
Mathematics版 - Tao已经找到初等证明了
相关主题
Bounded gaps between primes2008 Wolf Prize
外行评价一下Terence Tao 和Yitang Zhang谁更牛?摘星子煮酒论英雄
Tao 出招了丘成桐院士演讲:数学的内容、方法和意义
门外汉好奇请教:Faltings Theorem 和 Atiyah-Singer Index Theorem最近五十年数学界激动人心的时刻
some tales of mathematic!ans(184)问个我想了好些年的问题
some tales of mathematic!ans(184)老张的文章有几个部分貌似非常深
some tales of mathematic!ans(184)这里有想touch黎曼猜想的吗?
some tales of mathematic!ans(184)perfect number?
相关话题的讨论汇总
话题: type话题: zhang话题: vaughan话题: ii话题: tao
进入Mathematics版参与讨论
1 (共1页)
L*********s
发帖数: 3063
1
Terry Tao: one can use the Type I estimates to raise \sigma up to 1/6, which
closes off the Type III case completely and allows for a slightly more
elementary proof of Zhang’s theorem in that the full strength of Deligne’s
proof of the Weil conjectures is no longer needed
Ben Green:It means one could in principle teach the whole proof in a
graduate course.
Terry Tao:Just recording the results of a discussion I had with Ben on this
. It does look like Vaughan’s identity with U=V=x^{1/3}, together with a
Zhang-Type I estimate that works for \sigma=1/6, is enough to establish
Zhang
’s theorem; the Vaughan-Type II sums can be handled by Zhang’s Type I/II
analysis, and the Vaughan-Type I sums can be handled by either Zhang Type I/
II or Zhang Type 0, depending on the exact scales involved. So one does not
need either the Heath-Brown identity or Deligne’s theory to prove Zhang’s
theorem, just Weil’s bound on completed exponential sums.
m*****n
发帖数: 1631
2
佩服得一塌糊涂!
v*******e
发帖数: 11604
3
楼主翻译错了,a slightly more elementary proof of Zhang’s theorem只是比他的
初等一点点,不说明它是初等证明。
L*********s
发帖数: 3063
4
这些解析上的高等技术,比起Etale cohomology on topos来只能算是初等了

【在 v*******e 的大作中提到】
: 楼主翻译错了,a slightly more elementary proof of Zhang’s theorem只是比他的
: 初等一点点,不说明它是初等证明。

p*********g
发帖数: 5964
5
那你这些所谓的初等,高等要看对谁来说。

这些解析上的高等技术,比起Etale cohomology on topos来只能算是初等了

【在 L*********s 的大作中提到】
: 这些解析上的高等技术,比起Etale cohomology on topos来只能算是初等了
m****m
发帖数: 2211
6
老张说他的证明其实并不是使用的经典的方法
前面的证明大部分是经典的方法
证明的最后一部分用是很新的东西
是代数几何的东西
Tao这里说的是什么意思?难道是说老张后面的代数几何的东西可以不用?

which
’s
this

【在 L*********s 的大作中提到】
: Terry Tao: one can use the Type I estimates to raise \sigma up to 1/6, which
: closes off the Type III case completely and allows for a slightly more
: elementary proof of Zhang’s theorem in that the full strength of Deligne’s
: proof of the Weil conjectures is no longer needed
: Ben Green:It means one could in principle teach the whole proof in a
: graduate course.
: Terry Tao:Just recording the results of a discussion I had with Ben on this
: . It does look like Vaughan’s identity with U=V=x^{1/3}, together with a
: Zhang-Type I estimate that works for \sigma=1/6, is enough to establish
: Zhang

1 (共1页)
进入Mathematics版参与讨论
相关主题
perfect number?some tales of mathematic!ans(184)
为什么Tao在张益唐这个事件中象个局外人some tales of mathematic!ans(184)
看着tao和ben green的online seminar讨论的那么辛苦,老张为什么不去解释(指点)一下?some tales of mathematic!ans(184)
WEI ZHANG TO RECEIVE 2010 SASTRA RAMANUJAN PRIZEsome tales of mathematic!ans(184)
Bounded gaps between primes2008 Wolf Prize
外行评价一下Terence Tao 和Yitang Zhang谁更牛?摘星子煮酒论英雄
Tao 出招了丘成桐院士演讲:数学的内容、方法和意义
门外汉好奇请教:Faltings Theorem 和 Atiyah-Singer Index Theorem最近五十年数学界激动人心的时刻
相关话题的讨论汇总
话题: type话题: zhang话题: vaughan话题: ii话题: tao