Counting from Infinity, A film about Yitang Zhang and the twin prime conjecture, 终于公映了

Yitang Zhang

Alexander Grothendieck passed away on November 13, 2014, at the age of 86, in Saint-Girons.

He died Thursday at a hospital in the southwestern town of Saint-Girons, hospital officials said, without specifying the cause of death for privacy reasons. According to French daily Le Monde, Gothendieck had been living for decades in a hideaway home in the nearby village of Lasserre.

Grothendieck was a leading mind behind algebraic geometry — a field with practical applications including in satellite communications. In 1966, he was awarded the Fields Medal.

Grothendieck 离开数学圈后, 并非完全与世隔绝.

Yitang Zhang is giving the last invited talk at ICM 2014, “Small gaps between primes and primes in arithmetic progressions to large moduli”.

Yitang Zhang is giving the last invited talk 1

Yitang Zhang stepped onto the main stage of mathematics last year with the announced of his achievement that is hailed as “a landmark  theorem in the distribution of prime numbers”.

Yitang Zhang is giving the last invited talk 2

Yitang Zhang is giving the last invited talk 3

Opening Ceremony of ICM 2014

Martin Groetschel, Secretary-General of IMU, 在开幕式上的讲话说, IMU 有一些倡议. 这些打算之一是 adopt-a-graduate-student: IMU 会扶持发达国家的数学家, 这些数学家愿意给不那么发达国家的工作在相近领域的数学博士提供指导(mentorship).

Martin Groetschel 还指出, 韩国的数学出版物的数量当前是世界第 11 位, 但韩国数学家 1981 年发表在国际期刊上的论文仅仅只有 3 篇. 韩国从几乎一无所有, 建立了现在的数学传统, 仅仅过了一代人的时间.

1981 年成为国际数学联盟的最低等级第1军成员国的韩国时隔 33 年从援助受惠国成为供应国, 这将成为向全世界宣传韩国数学的契机.

ICM 开幕式的一个小插曲是, 戴着面具的舞蹈演员走上舞台时, Maryam Mirzakhani 的不到三岁的女儿 Anahita 发出恐怖的尖叫, 许久才平静下来. Timothy Gowers 有一个 6 岁的儿子.

The Fields Medal Committee for 2014 consisted of Daubechies, Ambrosio, Eisenbud, Fukaya, Ghys, Dick Gross, Kirwan, Kollar, Kontsevich, Struwe, Zeitouni and Günter Ziegler.

The program committee consisted of Carlos Kenig (chair), Bolthausen, Alice Chang, de Melo, Esnault, me, Kannan, Jong Hae Keum, Le Bris, Lubotsky, Nesetril and Okounkov.

Kyoto University professor Shigefumi Mori has been elected president of the International Mathematical Union(IMU), becoming the first head of the group from Asia.

The ICM executive committee for the next four years will be Shigefumi Mori (president), Helge Holden (secretary), Alicia Dickenstein (VP), Vaughan Jones (VP), Dick Gross, Hyungju Park, Christiane Rousseau, Vasudevan Srinivas, John Toland and Wendelin Werner.

### References

1. Timothy Gowers, ICM2014 — opening ceremony, August 13, 2014
2. ICM 2014

ICM 2014 Program

4 个数学家将获得本届大会的 Fields Medal.

1. A Transition Formula for Mean Values of Dirichlet Polynomials
2014,6.23./6.25. 9:30-11:30

2. 关于 Siegel 零点
2014.7.2.9:30-11:30

3. Distribution of Prime Numbers and the Riemann Zeta Function
July 8, 10, 2014 16:00-17:00, 镜春园82号甲乙丙楼的中心报告厅
July 15, 16:30-17:30 镜春园 78 号院的 77201 室.

4. 关于 Siegel 零点(2)
014.7.16./7.30./8.4./8.6. 9:30-11:30
N820

I’ve just received a book named Number Theory in the Spirit of Liouville by Kenneth S. Williams.

Number Theory in the Spirit of Liouville

Joseph Liouville is recognised as one of the great mathematicians of the nineteenth century, and one of his greatest achievements was the introduction of a powerful new method into elementary number theory. This book provides a gentle introduction to this method, explaining it in a clear and straightforward manner. The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others. All of the topics discussed have a rich history dating back to Euler, Jacobi, Dirichlet, Ramanujan and others, and they continue to be the subject of current mathematical research. Williams places the results in their historical and contemporary contexts, making the connection between Liouville’s ideas and modern theory. This is the only book in English entirely devoted to the subject and is thus an extremely valuable resource for both students and researchers alike.

• Demonstrates that some analytic formulae in number theory can be proved in an elementary arithmetic manner
• Motivates students to do their own research
• Includes an extensive bibliography

Preface
1. Joseph Liouville (1809–1888)
2. Liouville’s ideas in number theory
3. The arithmetic functions $$\sigma_k(n)$$, $$\sigma_k^*(n)$$, $$d_{k,m}(n)$$ and $$F_k(n)$$
4. The equation $$i^2+jk = n$$
5. An identity of Liouville
6. A recurrence relation for $$\sigma^*(n)$$
7. The Girard–Fermat theorem
8. A second identity of Liouville
9. Sums of two, four and six squares
10. A third identity of Liouville
11. Jacobi’s four squares formula
12. Besge’s formula
13. An identity of Huard, Ou, Spearman and Williams
14. Four elementary arithmetic formulae
15. Some twisted convolution sums
16. Sums of two, four, six and eight triangular numbers
17. Sums of integers of the form $$x^2+xy+y^2$$
18. Representations by $$x^2+y^2+z^2+2t^2$$, $$x^2+y^2+2z^2+2t^2$$ and $$x^2+2y^2+2z^2+2t^2$$
19. Sums of eight and twelve squares
20. Concluding remarks
References
Index.

## Review

“… a fascinating exploration and reexamination of both Liouville’s identities and “elementary” methods, providing revealing connections to modern techniques and proofs. Overall, the work contributes significantly to both number theory and the history of mathematics.”

J. Johnson, Choice Magazine

Publisher: Cambridge University Press (November 29, 2010)
Language: English
FORMAT: Paperback
ISBN: 9780521175623
LENGTH: 306 pages
DIMENSIONS: 227 x 151 x 16 mm
CONTAINS: 275 exercises

I’ve just received a book named Development of Elliptic Functions According to Ramanujan
by K Venkatachaliengar (deceased) , edited by: ShaunCooper , Shaun Cooper

Development of Elliptic Functions According to Ramanujan

This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter.

The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan’s work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.

## Contents:

• The Basic Identity
• The Differential Equations of $$P$$, $$Q$$ and $$R$$
• The Jordan-Kronecker Function
• The Weierstrassian Invariants
• The Weierstrassian Invariants, II
• Development of Elliptic Functions
• The Modular Function $$\lambda$$

Readership: Graduate students and researchers in Number Theory and Classical Analysis, as well as scholars and aficionados of Ramanujan’s work.

## Review

It is obvious that every arithmetician should want to own a copy of this book, and every modular former should put it on his ‘to be handled-with-loving-care-shelf.’ Reader of Venkatachaliengar’s fine, fine book should be willing to enter into that part of the mathematical world where Euler, Jacobi, and Ramanujan live: beautiful formulas everywhere, innumerable computations with infinite series, and striking manouevres with infinite products.

— MAA Reviews

The author was acquainted with many who knew Ramanujan, and so historical passages offer information not found in standard biographical sources. The author has studied Ramanujan’s papers and notebooks over a period of several decades. His keen insights, beautiful new theorems, and elegant proofs presented in this monograph will enrich readers.

— MathSciNet

The author has studied Ramanujan’s papers and notebooks over a period of several decades. His keen insights, beautiful new theorems, and elegant proofs presented in this monograph will enrich readers. italic Zentralblatt MATH

— Zentralblatt MATH

• Series: Monographs in Number Theory (Book 6)
• Hardcover: 184 pages
• Publisher: World Scientific Publishing Company (September 28, 2011)
• Language: English
• ISBN-10: 9814366455
• ISBN-13: 978-9814366458