Zhang, Shouwu
Overview
Works:  12 works in 40 publications in 2 languages and 1,461 library holdings 

Roles:  Redactor, Editor, Author 
Classifications:  QA564, 516.352 
Publication Timeline
.
Most widely held works by
Shouwu Zhang
Lectures on the arithmetic RiemannRoch theorem by
Gerd Faltings(
Book
)
4 editions published in 1992 in English and held by 378 WorldCat member libraries worldwide
4 editions published in 1992 in English and held by 378 WorldCat member libraries worldwide
The GrossZagier formula on Shimura curves by
Xinyi Yuan(
Book
)
13 editions published between 2011 and 2013 in English and held by 221 WorldCat member libraries worldwide
"This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the Birch and SwinnertonDyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the GrossZagier 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 Lseries by means of Weil representations. The GrossZagier 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 GrossZagier formula is reduced to local formulas. The GrossZagier 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
13 editions published between 2011 and 2013 in English and held by 221 WorldCat member libraries worldwide
"This comprehensive account of the GrossZagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of Lseries. The formula will have new applications for the Birch and SwinnertonDyer conjecture and Diophantine equations. The book begins with a conceptual formulation of the GrossZagier 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 Lseries by means of Weil representations. The GrossZagier 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 GrossZagier formula is reduced to local formulas. The GrossZagier 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 Lseries by
Henri Darmon(
Book
)
13 editions published between 2004 and 2010 in English and held by 191 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 GrossZagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the RankinSelberg method, arithmetic intersection theory, and much more
13 editions published between 2004 and 2010 in English and held by 191 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 GrossZagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the RankinSelberg method, arithmetic intersection theory, and much more
Positive line bundles on arithmetic surfaces by
Shouwu Zhang(
)
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Seminars on Congruent Problem by
Shouwu Zhang(
Visual
)
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
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
Seminars on Congruent Problem by
Shouwu Zhang(
Visual
)
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 StephenBirch and Monsky to products of two primes
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 StephenBirch and Monsky to products of two primes
A thousand years old problem and a million dollars prize by
Shouwu Zhang(
Visual
)
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
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(
Visual
)
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
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
CalabiYau theorem and algebraic dynamics by
Shouwu Zhang(
Visual
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
In this talk, Prof Zhang will first state a CalabiYau theorem for both complex and padic manifolds and applications to dynamical system on complex varieties in terms of preperiodic points. Then he will discuss dynamical ManinMumford conjectures with both supporting examples and counterexamples. This is a report of joint works with Xinyi Yuan, and Ghioca and Tucker respectively
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
In this talk, Prof Zhang will first state a CalabiYau theorem for both complex and padic manifolds and applications to dynamical system on complex varieties in terms of preperiodic points. Then he will discuss dynamical ManinMumford conjectures with both supporting examples and counterexamples. This is a report of joint works with Xinyi Yuan, and Ghioca and Tucker respectively
Shi yi de shu qing(
Book
)
1 edition published in 2004 in Chinese and held by 1 WorldCat member library worldwide
1 edition published in 2004 in Chinese and held by 1 WorldCat member library worldwide
The GrossZagier Formula on Shimura Curves by
Wei Zhang(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Heegner Points and Rankin L Series. Mathematical Sciences Research Institute Publications 49(
)
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin Lseries 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 Lseries 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 GrossZagier 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 RankinSelberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the GrossZagier formula
1 edition published in 2004 in English and held by 0 WorldCat member libraries worldwide
The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin Lseries 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 Lseries 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 GrossZagier 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 RankinSelberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the GrossZagier formula
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fewer
Audience Level
0 

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Related Identities
 Zhang, Wei 1981 Author
 Yuan, Xinyi 1981 Author
 Darmon, Henri 1965 Author Editor
 Faltings, Gerd Author
 Hong Kong University of Science and Technology Institute for Advanced Study
 Princeton University Editor
 RiemannRoch, Teorema de
 ebrary, Inc
 Princeton University Press Publisher
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