Number Theory @ SDU---Please Enjoy Here!

置顶讨论帖！

为避免大家在有些帖子下回复无关话题，特开辟此置顶讨论帖！大家有任何问题、体会、建议、意见、牢骚都可以上来发表，欢迎大家灌水！

这学期, 我们讨论Iwaniec的Spectral methods of Automorphic Forms, Second Edtion, GSM, Volume53, Amer. Math. Soc., Providence, 2002. 希望能讲完这本书,尽量都给出详细的证明.在讲课的同时,找一些大家刚兴趣的相关论文读读.

http://www.prime.sdu.edu.cn/courses/SpecThTraceF.htm

CIMPA Research School on Automorphic forms and L-functions [Aug 2010]

The CIMPA Research School will be held at Shandong University, Weihai Campus, China, during August 1-14, 2010, and will focus on Automorphic forms and L-functions. The research school is intended to higher education and research teaching staffs. The expected audiences are PhD students, young faculty members from universities in Asia. The expected number of participants (not including the speakers) is 50, among which 40 from China and 10 from other countries or districts. The school is sponsored by the CIMPA, the NSF of China, and Shandong University. For more information, please click http://www.prime.sdu.edu.cn/cimpaschool/welcome.htm

International Conference on Number Theory and Representation Theory

The International Conference on Number Theory and Representation Theory, organized by Professors Yangbo Ye and Jianya Liu, will be held at Shandong University, Weihai, China, during August 2-8, 2009. List of Invited Speakers: Andrew Booker (University of Bristol) Daniel Bump (Stanford University) Brian Conrey (American Institute of Mathematics) Patrick Gallagher (Columbia University) Dorian Goldfeld (Columbia University) Henryk Iwaniec (Rutgers University) Muthu Krishnamurthy (The University of Iowa) Philip Kutzko (The University of Iowa) Yuk-Kam Lau (The University of Hong Kong) Lawrence Morris (Clark University) Alberto Perelli (Universita di Genova) Janos Pintz (Renyi Institute of Mathematics) Kai-Man Tsang (The University of Hong Kong) Jie Wu (Universite de Nancy 1) The conference will focus on analytic number theory and group representation theory. In addition to the invited lectures there will be contributed talks. Talks will be on August 3 through August 7. For more informations, please click http://www.prime.sdu.edu.cn/cms1/index.php?modules=show&id=79 http://www.math.uiowa.edu/~yey/weihai09.html

Number Theory Seminars

(1)
Speaker: Yoshio Tanigawa, Nagoya University, Japan
Title: Modular forms, Apéry and other related numbers and analogues of Clausen formula
Venue: Room 309, Math Building
Time: 15:00-15:50, Wednesday, Mar 11, 2009

(2)
Speaker: Jie Wu, Universite de Nancy 1, France
Title: Power sums of Hecke's eigenvalues of newforms and their sign changes
Venue: Room 309, Math Building
Time: 16:00-16:50, Wednesday, Mar 11, 2009


ALL ARE WELCOME. 

Number Theory Colloquium

Speaker: Stephen Gelbart, Weizmann Institute of Science, Israel

Title: Langlands picture of automorphic forms and L-functions
Venue: Room 309, The Math Building
Time: 15:00-17:00
Date: Mar. 3, 6, 10, 13, 17, 19, 20, 24, 26, 27, 2009

ALL ARE WELCOME！

www.prime.sdu.edu.cn

Number Theory Colloquium

Speaker: Erez Lapid, The Hebrew University of Jerusalem, Israel

Title 1: Spectral analysis for Γ﹨Η
Venue: Room 309, The Math Building
Time: 15:00-17:00
Date: Feb. 17, 19, 20, 24, 26, 27; Mar. 3, 6, 10, 13, 2009

ALL ARE WELCOME！

www.prime.sdu.edu.cn

Distinguished Lecture Series

Speaker: Jean-Marc Deshouillers, Universite de Bordeaux 1, France

Title 1: Harmonic analysis in the study of some inverse additive problems
Venue: Room 309, Math Building
Time: 14:00-15:00, Monday, Nov. 17, 2008

Title 2: On the distribution of the values of positive multiplicative functions
Venue: Room 309, Math Building
Time: 14:00-15:00, Tuesday, Nov. 18, 2008

ALL ARE WELCOME！

www.prime.sdu.edu.cn

 

Workshop on Additive Number Theory 
                         
Organizer: Professor Jianya Liu, School of Mathematics, Shandong University

Speaker: Professor Tim Browning,
School of Mathematics, University of Bristol
Title: Density of rational points and del Pezzo surfaces

Speaker: Professor Jörg Brüdern,
Department of Mathematics, Université de Stuttgart
Title: The circle method and the theory of almost periodic functions
 
Speaker: Professor Trevor Wooley,
School of Mathematics, University of Bristol
Title: Waring's problem

Time:   August 16-26, 2008
Venue: School of Mathematics and Statistics,
            Shandong University, Weihai Campus

All ARE WELCOME! 

Description of Lectures for March 2009
> > >
I shall introduce the Langlands picture of automorphic forms and  L-functions by carefully surveying the known theory for GL(1). This means starting with Riemann's zeta-function, and progressing through Hecke's generaliztions of it in 1916. After doing this, I shall introduce the adeles and ideles of a number field. This will make it easier to discuss Artin's L-seies attached to a Galois group, his beautiful statement of abelian class field theory, and (his student) Tate's redoing of Riemann-Hecke L-functions in 1950. These results ultimately form part of the motivation of the general Langlands program.

大数学家Gelbart明年三月份要来一个月！大家要好好准备一下，主要内容是GL（1）上的。不过建议下学期大家还是轮流讨论一下S. Gelbart Automorphic Forms on Adele Groups ,至少前六章，大家应该知道！

Automorphic forms and L-functions 

Title: Automorphic forms and L-functions
Speaker: Yangbo Ye, The University of Iowa, Shandong University
Venue: Room 309
Time: 14:00,   June 30-July 18, 2008

ALL ARE WELCOME.

 Basic knowledge on Modular forms 

Title: Basic knowledge on Modular forms 
Venue: Conference Room 309
Time: 9：00 AM &2：00 PM, Sunday 6.29，2008

This lecture is a preparation for the study of modular forms.

ALL ARE WELCOME！

To 基地班和基础数学系的同学,

下面网页是这次期末考试试题，欢迎大家浏览下载：

http://numbertheory.blogbus.com/files/12144933540.pdf

http://numbertheory.blogbus.com/files/12144933541.pdf

这次考试，因为有部分试题是我们课后作业和书上的定理，平时认真做作业、听课的同学还都是考的很好的。但是满分的并不多，主要是有些同学审题读题不够仔细、做题思路不够清晰、考虑问题不够全面而至。鉴于大家做的不错，我批卷基本上是比较严格一点的。按扣分算的。下面就每个题的详细得分点扣分点，给大家解释一下：

1，满分10分，正确答案 a=144,b=24或a=72,b=48。这是一个基本的计算题，大家基本都能得满分的。但是有些同学，看题不够认真，得到了4个答案，这要扣2分（这有点冤，但是既然题目里面要求了，就应该考虑的）；有的只得到一个正确答案，这要扣3分。

2，满分25分。（1）满分5分。这一个要利用数论函数可乘性的一个性质：对因子求和和对素因子求乘积之间的一个等式（课本p24，（30）式），就出来了！用其他方法，我没有发现做对的。（2）满分10分。这个题有很多同学，把（1）结果带入，然后直接把里面展开，说里面求和项是有限项云云，故是O（1），从而整个求和项是O（x），这样做根本上是错的！里面求和项个数是和n有关的，n在变，不能直接认为是有限项！我说过很多次，对大家来说只有两种初等方法求数论函数的均值估计：求和号交换次序和利用Abel定理分部求和！带入（1），然后交换次序，把取整分成本身减去小数部分，往下顺理成章的估计就完了。但是也有人直接到这一步就得出答案，而没有说明前面可以放大到一个收敛级数和估计余项的，要扣5分！（3）满分10分。这一小题利用前面的结论和分部求和，很容易就得到答案，即使前两题不会做的同学，这个有的也能的满分！不利用Abel求和交换次序也能得到正确答案。

3，满分20. （1）满分5分。叙述Abel求和公式这个基本上都会，但是也有的同学写成了加号，扣2分。（2）满分15分。这是Mertens Theorem书上有详细的证明过程。这里的难点是要估计余项和指出无穷积分是收敛的、和具体给出C的含义（实际上C是唯一确定的,称为Mertens Constant，0.2614972128...）！没有指出或者隐含这C应该是1-loglog2+A，A是那个无穷积分，要扣1分；没有估计从x积到无穷大等于O（1/logx）,要扣3分。用了一次Abel公式，只把主项算出来，下面就稀里糊涂的就直接给出答案来，一看就是想懵我，这样没有估计余项的只能得到10分。

4，满分10分，正确答案x≡19（mod35）。这个题大家做的非常好，可能只有3、4个同学没有得满分吧，利用代入法就很容易得到答案的。这是一个基本的同余方程，不会做的，可以挖个坑把自己埋了！呵呵

5, 满分15分，正确答案p为2、3或6n+1型素数。这个题是同学得分比较差的一道，很多同学忽略了2和3，要扣2分，少一个扣一分；只得到3n+1型素数，要扣4分；得到p为2或3n+1型素数要扣3分；得到p为2、3或3n+1型素数，不扣分。没有正确得到答案，如果正确应用了二次互反律，至少得4分。

6, 满分20分，（1）满分5分，正确答案为8个原根，3是最小正原根。这一问基本都做对了，有三个同学算对了原跟个数没有算对最小正原根，得3分。（2）满分5分，指标为8. 这一步就是带入直接验证即可。（3）满分10分，x≡9，15，8,2（mod17）。没有化成最简单mod17的形式要扣2分，有几个同学只得到为3幂次，没有化成模17的形式。当然你得到x≡2,-2,9,-9（mod17）不会扣分的！

后记：给大家写这么详细解释清楚，是因为有些同学可能以为自己要考满分的试卷，怎么只得了98或更低了哪？大家放心，基本考得都很好！有4、5个同学卷面分做的不太好，但是参考一下平时成绩作业考勤等，大家都过了！具体成绩大家可以过两天上网自己查的，问我的话，我也大都记不得的。希望大家不要太在乎成绩本身。

给大家开初等数论课程，不是希望你们以后要学数论，也不是希望以后你们要学基础数学！我想目的就是要大家对数论有一个概括的了解和接受到一些严格严谨的数学训练，进而培养一个好的数学素养！因为数论是一门严肃的数学！例如，一个数论函数的取值往往是很不规律的，但是它的均值估计往往有很好的性质，你要能看到它背后隐藏的算术含义和所体现的数学的内在的本质的美！特别是像素数的分布的一些规律！例如：按照大家做题的思路，第二大题第二问我们可以得到估计的主项是Cx,C是一个确定的常数，你应该看出来n/\phi(n)平均起来大小是1，也就是说n和\phi(n)的阶基本上差不多；像第三大题第二问，由这个渐进公式，能看出很多东西，素数有无穷多个，素数倒数和发散，素数出现的概率是1/logx....

以后如果有人问你或者面试你:你认为数论里面哪些结果是漂亮的？我希望你能回答素数分布的一些定理像素数定理切比雪夫定理等，和二次互反律。这也是整个现代数论的的基础！

另外和同学们处了半年，对大家也有了一个简单的了解吧！希望大家首先把我看成你们的朋友、学长，然后才是纪老师。下学期，同学们就面临着很多选择：考研保研出国工作等等，无论如何希望大家要努力争取要积极乐观，做一个有责任心能担当的人！与各位共勉之！^_^

FINDING MEANING IN ERROR TERMS
BARRY MAZUR
In memory of Serge Lang
Introduction

Four decades ago, Mikio Sato and John Tate predicted the shape of probability distributions to which certain “error terms” in number theory conform. Their prediction—known as the Sato-Tate Conjecture—has been verified for an important class of cases thanks to the recent work of Laurent Clozel, Michael Harris, and Richard Taylor [3], and of Michael Harris, Nicholas Shepherd-Barron, and Richard Taylor [18], combined with Richard Taylor’s most recent [54], which establishes this advance in our understanding.

Part of the beauty of this breakthrough is how it pulls together progress made over the past quarter century and work from significantly different viewpoints—from the theory of automorphic representations, from algebraic geometry, and from Galois deformation theory—a demonstration, yet again, of the intense unity of mathematical thought.

My aim is to discuss, in concrete terms, two “sample problems”—one still open, and one settled by the recent work—that give rise to error terms, about which the Sato-Tate Conjecture makes precise predictions.

http://www.ams.org/bull/2008-45-02/S0273-0979-08-01207-X/home.html

On a Theorem of Daboussi

Title: On a Theorem of Daboussi
Speaker: Imre Kátai, Eötvös Loránd University, Hungary
Venue: Room 201
Time: 16:00, Monday, May 19, 2008

ALL ARE WELCOME. 

Central Value of Automorphic L-functions

Title: Central Value of Automorphic L-functions
Speaker: Zhengyu Mao, Rutgers University, USA
Venue: Conference Room 309
Time: 10:30, Thursday, Apr 3, 2008

ALL ARE WELCOME

Breakthrough in the Study of L-functions

A new mathematical object was revealed today during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.
The news caused excitement at the AIM workshop attended by 25 of the world's leading analytic number theorists. The work is a joint project between Ce Bian and his adviser, Andrew Booker. Booker commented that, "This work was made possible by a combination of theoretical advances and the power of modern computers." During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results.

 "This breakthrough opens a door to the study of higher degree L-functions," said Dennis Hejhal, Professor of Mathematics at the University of Minnesota and Uppsala University. "It's a big advance" added Harold Stark of the University of California, San Diego, who, 30 years ago was the first to accurately calculate second degree transcendental L-functions. "I thought we were years away from doing this. The geometry of what you have to do and the scale of the computation are orders of magnitude harder."

There are two types of L-functions: algebraic and transcendental, and these are classified according to their degree. The Riemann zeta-function is the grand-daddy of all L-functions. It holds the secret to how the prime numbers are distributed, and is a first degree algebraic L-function. The Riemann Hypothesis, announced in 1859 and today the most important of all unsolved math problems, is an example of something that should be true for EVERY L-function. Michael Rubinstein from the University of Waterloo, a participant at the workshop, quickly tested and confirmed the Riemann Hypothesis for the first few zeroes of this newly minted L-function. Rubinstein, along with William Stein of the University of Washington, will direct a new initiative to systematically chart L-functions; this project has been recommended for funding by the National Science Foundation. "The techniques developed by Bian and Booker open up whole new possibilities for experimenting with these powerful and mysterious functions and are a key step towards making our group project a success." Rubinstein added.

"It's a big step toward our understanding the 'world of L,' which is where most of the secrets of number theory are kept." said Brian Conrey, Director of AIM.

Dorian Goldfeld, Professor of Mathematics at Columbia University summarized the excitement, saying ``This discovery is analogous to finding planets in remote solar systems. We know they are out there, but the problem is to detect them and determine what they look like. It gives us a glimpse of new worlds."

for more information, see http://www.aimath.org/news/gl3/.

Math Courses in Number Theory Introduction to Commutative Algebra Venue: Room 102, Math North Building Time: Every Wednesday, 5-7 Advanced Analytic Number Theory Venue: Room 201, Math North Building Time: Every Tuesday, 2-4 Class Field Theory Venue: Room 201, Math North Building Time: Every Friday, 1-3

On Some Topics in Automorphic Representations

Title: On Some Topics in Automorphic Representations 
Speaker: Dihua Jiang, University of Minnesota, USA
Venue: Room 309
Time: 10:10, Wednesday, Jan 2, 2008

Gross-Zagier Formula

Title: Gross--Zagier formula
Speaker: Tonghai Yang, University of Wisconsin, USA
Venue: Room 309
Time: 16:00, Monday, Dec. 24, 2007

History of irrational and transcendental numbers

Topic: History of irrational and transcendental numbers Speaker: M. Waldschmidt, Université Pierre et Marie Curie Paris VI, France Venue: Room 415, Lizong Building Time: Friday, Nov. 30, 2007, 18:30 Abstract: The transcendence proofs for constants of analysis are essentially all based on the seminal work by Ch. Hermite: his proof of the transcendence of the number e in 1873 is the prototype of the methods which have been subsequently developed. We first show how the founding paper by Hermite was influenced by earlier authors (Lambert, Euler, Fourier, Liouville), next we explain how his arguments have been expanded in several directions: Pade approximants, interpolation series, auxiliary functions.

下面是皮庆华有感而发的讨论。欢迎大家讨论

其实就是关于学习做学问“博”和“精”的问题. 像我们现在学的代数数论解析数论椭圆曲线都是非常基本的东西，这相当与“博”的部分。看最新的科研论文，就相当于“精”的部分。

关于博和精，华罗庚有几句比较精确的比喻，好像是说如果把做学问当作伐木，那斧头的前面的韧就相当于你学问的精，后面的斧头的厚度就相当于你学问的博。大意如此！

博而后精是治学成功之路！数学是一个长线学科，需要积累，所谓的厚积薄发所谓此。耍点小聪明做不了大学问的！治学的最终目标是博学而精通，要有相当博的精，才算的真的精；要有相当精的博，才算是真的博。蜻蜓点水式的博不是博，坐井观天式的精不算精。而只是做到有所取舍，才能达到精博得治学的境界。


>Subject: 一次关于学习的聊天
>Date:Thu, 22 Nov 2007 03:48:28 +0800
>
>师兄：
> 晚上和朋友聊天后写了点东西，你看看适不适合发到你BLOG上。
>
>
今天晚上和舍友聊天，原本是聊他出国的平均成绩来着，结果话题慢慢扯到学习上了。
> 觉得很有意思，发出来给大家分享一下。
>

> 他虽然喜欢数学，不过计算机编程能力似乎更强。
>
> 开始的话题是关于他出国的，他想念数学专业的DOCTOR，我持否定意见。
> 因为不只是我，认识他的人都觉得他更适合去读计算机专业。
> 如果出去后再把大部分时间花到计算机上，非常不值得。
> 再说了，国外是很忌讳挂着数学专业名号出去转计算机的。
>
> 他说自己出去后会专心学好数学，将来要做数学与计算机之集大成者。我说不可能。
> 不论是计算机编程，还是数学研究，都是要耗费很大的精力和时间的。
> 学好任何一门，你都要保证在长时间内该学科的时间占有率达到70%以上，
> 两门学科对半分时间，行不通。
>
> 然后他举例，诸如冯.诺依曼等伟大的计算机学家都是由数学家转的。
> 我反驳说那是在计算机刚作为新兴学科独立的时候。
> 现在已经不比以前，不论是计算机还是数学，都发展出了细密的分支和严谨的研究方式，
> 两行都精通是行不通的。仅仅对计算机编程这条路，要成为规划大型项目的顶级分析师，
> 没有数以万计的程序来锤炼是不可能的；更不用说成为数学某个领域的大师级人物了。
>
> 他举例说计算机专业的导师很喜欢要数学专业的学生，
> 如图形学喜欢要代数几何的，密码学喜欢要数论的。
> 可惜那不应该算是数学了，他们要的仅仅是数学知识的一个应用。
> 再说了，除去赚钱不说，代数几何和数论，都要比计算机图形和密码要有趣的多。
>
> 话题转移到代数和代数几何学上。
> 谈胜利老师在华师大曾经说过，代数几何要学5年才能做东西。他不信。
> 对于一门学科，它的名词说起来也许都不陌生，几十分钟就把其过去现在将来描述清楚。
> 但为啥简简单单的几十分钟，要放在一本长达500多页的书里去说呢？
> 因为将来要出论文，开拓新领域，恰恰靠的是在深刻理解500多页的书的基本功上面。
> （- -|||....我自己的解析数论，是的好好抽时间认真重新学一下...）
>
> 之后他提出，做二流的数学家，能看懂最新的的成果就行。
> 我说一篇好的论文出来后，超一流的数学家会立即认识到它的价值，继而能根据文章，
> 规划学科将来的发展方向；一流的数学家会根据超一流数学家的规划去进行完善；
> 二流的数学家会在完善的基础上去进行细枝末节的补充...很可惜，如果那样分心，
> 到时候所看懂的仅仅只能是三流数学家也懂得的时候了。
> 而且即使是看懂，也要花费大量的时间去学习新的理论和工具。
> 拿Fermat大定理来说，之前思路是有的，就是部分Shimura-Taniyama猜想的问题。
> 不过仅有wiles不怕这个东西难，花了八年时间去证明。
> 但为了理解这个证明，国际数学家大会还专门花了一段时间去学习呢。
>
> 最后他说，学的数学挺杂的，不论是偏向实际的代数拓扑，还是抽象的广义度量空间。
> 他有个想法，把这两种东西花时间融合起来，然后应用到计算机上去。
>
我引用WuJie教授的话反驳，陈景润的1+2之所以算是一个突破，是因为他有一个新的想法；
> 但想法在实现中却产生了新的难题；他是解决难题后才有了1+2的成就。
> 往往一个好的想法，并不能保证实现起来一帆风顺...
>
> 最后我总结，产生这种想法是因为年轻。
> 想当初刚入学的时候，我也想是计算机和数学一把抓的，
> 可实际发现，代数数论和解析数论两者仅抓一门就够我忙的了，更别提什么计算机了……
> 随着年龄的增加，抓住自己真想要的，放弃需要放弃的东西，也许就意味着成长吧。
>
> 之后躺在床上，想了很多。
>
> 1.我也想代数数论、解析数论、算数几何三者一起抓……
> 2.平常师兄和刘老师发给大家的，代表数论研究最新方向的论文，很少看……
> 3.原本以为代数数论中的WARING问题会很简单，仅仅是个移植的问题……
>
4.在搜索新论文可做的东西的时候自己一头雾水，但吕师兄很容易找了两篇的文章给我……
>
> 然后就有了这个邮件。
>
> qhpi,于11.22深夜
>

Seminars in number theory

Title:   Distribution of primes, sieve methods and Chen's contributions
Speaker: Jie Wu, Université Henri Poincaré (Nancy 1), France
Venue:   Room 309
Time: &...

 

Distribution of primes, sieve methods and Chen's contributions

Title: Distribution of primes, sieve methods and Chen's contributions
Speaker: Jie Wu, Université Henri Poincaré (Nancy 1), France
Venue: Room 309
Time: TBA
Abstract: This course consists of 4 one and half hour talks. I shall describe Chen's main works on Goldbach's conjecture and the existence of quasi-primes in short intervals. My aim is not only to present Chen's results but also discuss in depth his contribution to the sieve theory. In the first talk, important problems on distribution of primes and principal tools in the sieve theory (before Chen) will be introduced, which are useful for the next three sessions. In the second and the third talks, I shall present Chen's two famous theorems on Goldbach's conjecture. Finally we shall discuss Chen's proof for the existence of $P_2$ in short intervals in the last talk. Meanwhile some recent developments in these questions are mentioned. 

 

A large sieve inequality of Elliott-Montgomery-Vaughan type for automorphic forms and two applications

Topic: A large sieve inequality of Elliott-Montgomery-Vaughan type for automorphic forms and two applications
Speaker:   Jie Wu, Université Henri Poincaré (Nancy 1), France
Venue: Room 309
Time: TBA
Abstract: In this talk, we shall present a large sieve inequality of Elliott-Montgomery-Vaughan type for Fourier coefficients of newforms. As applications, we shall give a significant improvement on the principal result of Duke & Kowalski on Linnik's problem for modular forms in the case of squarefree levels, and prove an upper bound result which is part of the first   Montgomery-Vaughan conjecture in the context of automorphic L-functions. All are welcome! 

下面仅以我个人的观点和喜好谈谈对数论的看法,学习需要的预备知识和一些参考书。仅供一些本科生研究生和喜欢数论而暂时还没有入门的朋友参考；如果你是专家，请马上出门左转！

 

一，数论的内容和方法

 

数论按研究对象可以分成两种, 一种是素数分布,一种是不定方程；数论按研究方法可以粗略地分成三种,  解析数论,代数数论和算术代数几何（组合数论，计算数论等也是数论的重要部分，笔者对此知识不了解，也不是特别感兴趣，在此均不涉及）。当然，历史地来看一个经典的问题的完全解决往往是综合地应用了多种研究方法：像高斯虚二次域的类数问题，里面有分析，有代数当然更有椭圆曲线的应用；费尔马问题当然更是如此。

推荐大家下载BBC拍摄的电影Fermat's Last Theorem，里面介绍了FLT的历史，采访了很多数学家Katz，Ribet，Sarnak，Shimura， Conway，Coats等等。当然主角是一个略显羞涩的中年人---Wiles！讲到在偷偷证明FLT的七年里的心历路程，动情处几欲落泪！

http://lib.verycd.com/2006/02/09/0000089039.html

Mini Course on Modualr forms

Title: Modular forms in one variable
Speaker: W. Kohnen, Universitat Heidelberg, Germany
Venue: Room 309
Date: Sep 10--Sep 20;   Monday, Tuesday, Thursday
Time: 14:00--15:00, 15:15--16:15
Abstract: We will introduce some of the basic features of the theory of modular forms in one variable. This in particular includes the modular group and its action on the upper half-plane, reduction theory, examples of modular forms and cusp forms (Eisenstein series, theta series), the valence formula and its applications, the basic modular invariant j, Hecke operators, Hecke L-functions, non-holomorphic Eisenstein series and applications. No pre-knowledge of modular forms is supposed. However, some basic knowledge of complex function theory will be assumed. 

Summer School on Arithmetic

School of Mathematics and System Sciences
Shandong University, Jinan

Organizer: Jianya Liu
Date: Aug 1-Sep 3, 2007
Venue: Conference Room 309


Yonggao Chen, Nanjing Normal University
Title：Dynamics of  an Arithmetic Function and Distribution of Primes

Shigeru Kanemitsu, Kinki University, Japan
Title: (1) Class field theory through examples -- for non-experts
        (2) Arithmetic Fourier series

A. V. Kumchev, Towson University, USA
Title: Exponential Sums over Primes and their Applications
Date: Jul. 26, 31
Time: 15:00-16:00

Erez Lapid, Hebrew University, Israel
Title: TBA

Ehud de Shalit, Hebrew University, Israel
Title: p-adic uniformization
Date: Aug 21, 2007
Time: 14:00-15:00

Yoshio Tanigawa, Nagoya University, Japan
Title: Bounds for double zeta-functions

Xianke Zhang, Tsinghua University
Mini course: Algebraic Number Theory
Date: Aug 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, Sep. 2, 3
Time: 14:00-15:00, 15:15-16:15 

 www.prime.sdu.edu.cn

清华大学张贤科教授将于18日在数学院309，开设为期24个学时的代数数论短期课程。时间初步定在下午2：00--4：15，中间休息一刻钟。将会为张老师在数学院安排一个专家室，大家可向张老师预约时间，请教学习中遇到的任何问题。张老师可能会按照他的那本代数数论书的某些章节讲，如果想看那本书的话：新版山大南门小树林书店有卖，旧版网上有电子版，找不到的可向小新要. ^_^

希望大家以后无论课上课下都踊跃一点，积极主动地向国内外来访的专家虚心地学习，勇敢问问题，甚至找其聊聊天都可以。作为一个学生，即使问些很trivial的问题，相信也不会有人笑话的. ^_^

Date: Aug. 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, Sep. 2, 3
Time: 14:00-15:00, 15:15-16:15
Venue: Room 309 

看来和素数定理有点关系的数学家，都高寿啊！象Hadamard 活到98，Vallée Poussin 96岁，连Erdös也80多啊。

Atle Selberg, 1917-2007

Atle Selberg, who had a major influence in mathematics and especially in analytic number theory during the 20th century, died on August 6. Born on June 14, 1917, in Langesund, Norway, he received his Ph.D. in 1943 from the University of Oslo. He is perhaps best known for his work on the zeros of the Riemann zeta function, for which he was awarded a Fields Medal in 1950, and for his elementary proof of the prime number theorem. The impact of his work can be seen in the many mathematical terms that bear his name: the Selberg trace formula, the Selberg sieve, the Selberg integral, the Selberg class, and the Selberg zeta function. Since the late 1940s he has been on the faculty of the Institute for Advanced Study in Princeton, and he retired in 1987. His honors include the 1986 Wolf Prize in Mathematics. The biography of Selberg on the MacTutor History of Mathematics web site has further details about his life. [Item posted 8/7/07]