Zhang, ShouwuOverview
Most widely held works by
Shouwu Zhang
The GrossZagier formula on Shimura curves
by Xinyi Yuan
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13 editions published between 2011 and 2013 in English and held by 419 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
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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 GrossZagier formula and its developments. It touches on the theory of complex multiplication, automorphic forms, the RankinSelberg method, arithmetic intersection theory, and much more
Lectures on the arithmetic RiemannRoch theorem
by Gerd Faltings
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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
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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 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
Positive line bundles on arithmetic surfaces
by Shouwu Zhang
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2 editions published in 1991 in English and held by 2 WorldCat member libraries worldwide
Seminars on Congruent Problem
by Shouwu Zhang
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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
CalabiYau theorem and algebraic dynamics
by Shouwu Zhang
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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
A thousand years old problem and a million dollars prize
by Shouwu Zhang
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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
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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
Heegner points and Rankin Lseries
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1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Seminars on Congruent Problem
by Shouwu Zhang
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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
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Book
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1 edition published in 2004 in Chinese and held by 1 WorldCat member library worldwide more
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Chang, Shouwu.
Chang Shouwu 1962....
Shouwu Zhang.
Zhang, Shouwu
Zhang, Shouwu 1962
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