WorldCat Identities

Zhang, Shouwu

Overview
Works: 12 works in 38 publications in 2 languages and 1,178 library holdings
Roles: Redactor, Editor
Classifications: QA242.5, 516.352
Publication Timeline
Key
Publications about  Shouwu Zhang Publications about Shouwu Zhang
Publications by  Shouwu Zhang Publications by Shouwu Zhang
Most widely held works by Shouwu Zhang
The Gross-Zagier formula on Shimura curves by Xinyi Yuan ( )
13 editions published between 2011 and 2013 in English and held by 419 WorldCat member libraries worldwide
"This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and Swinnerton-Dyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations with rational coefficients attached naturally to abelian varieties parametrized by Shimura curves. This is followed by a complete proof of its coherent analogue: the Waldspurger formula, which relates the periods of integrals and the special values of L-series by means of Weil representations. The Gross-Zagier formula is then reformulated in terms of incoherent Weil representations and Kudla's generating series. Using Arakelov theory and the modularity of Kudla's generating series, the proof of the Gross-Zagier formula is reduced to local formulas. The Gross-Zagier Formula on Shimura Curves will be of great use to students wishing to enter this area and to those already working in it."--Publisher's website
Heegner points and Rankin L-series by Henri Darmon ( Book )
11 editions published between 2004 and 2010 in English and held by 374 WorldCat member libraries worldwide
This title presents a collection of 13 articles by many of the leading contributors in the field on the history of the Gross-Zagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, and much more
Lectures on the arithmetic Riemann-Roch theorem by Gerd Faltings ( Book )
4 editions published in 1992 in English and held by 374 WorldCat member libraries worldwide
Heegner Points and Rankin L Series. Mathematical Sciences Research Institute Publications 49 ( )
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many generalisations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. This volume, based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, is a collection of thirteen articles written by many of the leading contributors in the field, having the Gross-Zagier formula and its avatars as a common unifying theme. It serves as a valuable reference for mathematicians wishing to become further acquainted with the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula
Positive line bundles on arithmetic surfaces by Shouwu Zhang ( Book )
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Seminars on Congruent Problem by Shouwu Zhang ( )
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this talk, the speaker will first discuss the relation between the congruent number problem and elliptic curves y2 = x3 - x. A solution assuming the BSD conjecture will be described
Calabi-Yau theorem and algebraic dynamics by Shouwu Zhang ( )
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
In this talk, Prof Zhang will first state a Calabi-Yau theorem for both complex and p-adic manifolds and applications to dynamical system on complex varieties in terms of preperiodic points. Then he will discuss dynamical Manin-Mumford conjectures with both supporting examples and counterexamples. This is a report of joint works with Xinyi Yuan, and Ghioca and Tucker respectively
A thousand years old problem and a million dollars prize by Shouwu Zhang ( )
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Do you know the area of a triangle? Do you know how to construct all right triangles with rational sides? If you know both, then try to solve a problem raised by Arabs over 1040 years ago: find a method to determine a positive integer n to be the area of a rational right triangle. Such a number is called a congruent number. Is 1 a congruent number? What about 5 or 7? After 1000 years, we still could not solve this problem. But we know it will follow from another unsolved problem which has a prize US$1,000,000
Seminars on Congruent Problem by Shouwu Zhang ( )
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this talk, the speaker will describe a method of Heegner to solve the equation y2 = x3 - x using modular parametrizations. In particular, Heegner showed that a prime p is a congruent number if it is 5 or 7 modulo 8. Such a work has been generalized by Stephen-Birch and Monsky to products of two primes
Heegner points and Rankin L-series ( )
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Seminars on Congruent Problem by Shouwu Zhang ( )
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
In this talk, the speaker will describe recent work of Prof Ye Tian (Morningside Center of Mathematics, Chinese Academy Sciences) who produced a large class of congruent numbers with arbitrary many prime factors
Shi yi de shu qing ( Book )
1 edition published in 2004 in Chinese and held by 1 WorldCat member library worldwide
 
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Audience level: 0.77 (from 0.00 for Heegner Po ... to 1.00 for Positive l ...)
Alternative Names
Chang, Shou-wu.
Chang Shou-wu 1962-....
Shouwu Zhang.
Zhang, Shou-wu
Zhang, Shou-wu 1962-
Languages
English (37)
Chinese (1)
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