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《代数函数与Abelian函数》是2009年8月1日世界图书出版公司出版的图书，作者是美国)莱恩(Lang.S.哥距图等)。
- 书名 代数函数与Abelian函数
- 作者 美国)莱恩(Lang.S.)
- 装帧 平装
- 开本 24开
图书信息
出读换根久针吧轻灯下称段版社: 世界图书出来自版公司; 第2版 (2009年8月1日)
外文书名: Introduction to Algebraic and Abelian Functions
平装: 169页
正文语种: 英语
开本: 24
ISBN: 75100校呢损底国洋形或告育0487X, 9787510004872
条形码: 9787510004872
尺寸: 22.2 x 14.8 x 1.2 cm
重量: 240 g
作者简介
作者:(美国)莱恩(Lang.S.)
内容简介
《代数函数与Abelian函数(第2版)(曲功洋刻视言状氢语英文版)》讲述了:This short book g些困土析划试械龙诗ives an introdu毫青风坐告他论培院研春ction to algebraic and abel布往ian functi军脸如ons, withempha山客点sis on the complex analytic point of view. It could be used for a course or seminar addressed to s批图仅病危宗烟econd year graduate s来自tudents.
The goal is the same as that of the first edition, although I hav360百科e made a number of additions. I have used the W责特配境eil proof of the Riemann-Roch the 意析括充物叫乙石矿事抗orem since it is efficient and acquaints the reader with adeles, which are a very useful tool pervading number theory.
Th苦务e proof of the Ab适几张永到el-Jacobi theorem is that given by Artin in a seminar in 1948. As far as I know, the ve殖剧握衣提措间向权且ry simple proof for the Jacobi inversion theorem is due to him. The Riemann-R被och theorem and the Abel-Jacobi theorem could form a one semester course.
The Riemann relations which come at the end of 既the treatment of Jacobi's theorem form a br践战剧顶语哥级乎他idge with the second part whi物环站ch deals with abelian functionsand thet另a functions. In May 1949, Weil gave a boost to the basic theory 经过应构系战久迅裂湖of theta functions in a famous Bourbaki seminar talk. I have followed his exposition of a proof of Poincare that to each divisor on acomplex torus therecorresponds a theta function on the universal covering space. However, the correspondence between divisors and theta functions is not needed for the linear theory of theta functions and the projective embedding of the torus when there exists a positive non-degenerate Riemann form. Therefore I have given the proof of existence of a theta function corresponding to a divisor only in the last chapter, so that it does not interfere, with the self-contained treat- ment of the linear theory.
目录
Chapter Ⅰ The Riemann-Roch Theorem
1. Lemmas on Valuations
2. The Riemann-Roch Theorem
3. Remarks on Differential Forms
4. Residues in Power Series Fields
5. The Sum of the Residues
6. The Genus Formula of Hurwitz
7. Examples
8. Differentials of Second Kind
9. Function Fields and Curves
10. Divisor Classes
Chapter Ⅱ The Fermat Curve
1. The Genus
2. Differentials
3. Rational Images of the Fermat Curve
4. Decomposition of the Divisor Classes
Chapter Ⅲ The Riemann Surface
1. Topology and Analytic Structure
2. Integration on the Riemann Surface
Chapter Ⅳ The Theorem of Abel-Jacobi
1. Abelian Integrals
2. Abel's Theorem
3. Jacobi's Theorem
4. Riemann's Relations
5. Duality
Chapter Ⅴ Periods on the Fermat Curve
1. The Logarithm Symbol
2. Periods on the Universal Covering Space
3. Periods on the Fermat Curve
4. Periods on the Related Curves
Chapter Ⅵ Linear Theory of Theta Functions
1. Associated Linear Forms
2. Degenerate Theta Functions
3. Dimension of the Space of Theta Functions
4. Abelian Functions and Riemann-Roch Theorem on the Toru
5. Translations of Theta Functions
6. Projective Embedding
Chapter Ⅶ Homomorphisms and Duality
1. The Complex and Rational Representations
2. Rational and p-adic Representations
3. Homomorphisms
4. Complete Reducibility of Poincar
5. The Dual Abelian Manifold
6. Relations with Theta Functions
7. The Kummer Pairing
8. Periods and Homology
Chapter Ⅷ Riemann Matrices and Classical Theta Functions
1. Riemann Matrices
2. The Siegel Upper Half Space
3. Fundamental Theta Functions
chapterⅨ
Involutions and Abelian Manifolds of Quaternion Type
1. Involutions
2. Special Gnerators
3. Orders
4. Lattices and Riemann Forms on Determined by Quaternion Algebras
5. Isomorphism Classes
chapteⅩ
Theta Functions and Divisors
I. Positive Divisors
2. Arbitrary Divisors
3. Existence of a Riemann Form on an Abelian Variety
Bibliography
Index
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