复分析-第2版

1星价 ¥76.5 (8.6折)

2星价￥76.5 定价￥89.0

作者：EberhardFreitag，Rol

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学 > 数学分析

买过本商品的人还买了

暂无评论

图文详情

ISBN：9787510077838
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24开
页数：532
出版时间：2014-07-01
条形码：9787510077838 ; 978-7-5100-7783-8

本书特色

　　this book is a translation of the forthcoming fourth edition of our german book "funktionentheorie p' (springer 2005). the translation and the latex files have been produced by dan fulea. he also made a lot of suggestions for improvement which influenced the english version of the book. it is a pleasure for us to express to him our thanks. we also want to thank our colleagues diarmuid crowley, winfried kohnen and jorg sixt for useful suggestions concerning the translation.

内容简介

本书是一部讲述经典复分析的综合教程，此处经典的意思是省去了层理论和上同调方法。前四章是对复分析基本结果的集中表述，在这些标准材料之后，作者介绍了椭圆函数和椭圆模函数和这个领域的*漂亮的结果。书中以在解析数论中的应用作为圆满结束，其中有如素数数论这样很吸引人的专题。本书的自称体系，所需要的内容都进行了完整的讲述，几乎不需要预备知识。400多道练习题，大量的题解提示和众多图表，使得这本书成为学习经典复分析入门的教材。

ⅲ　sequences and series of analytic functions, the residue　theorem
ⅲ.1 uniform approximation
ⅲ.2 power series
ⅲ.3 mapping properties of analytic functions
ⅲ.4 singularities of analytic functions
ⅲ.5 laurent decomposition　a appendix to iii.4 and iii.5
ⅲ.6 the residue theorem
ⅲ.7 applications of the r,esidue theorem

ⅳ construction of analytic functions
ⅳ.1 the gamma function
ⅳ.2 the weiers'rrass product formula
ⅳ.3 the mitrrac_leffler partial fyaction decomposition
ⅳ.4 the riemann mapping theorem
a appendix : the homotopical version of the cauchy　integral theorem
b appendix : a homological version of the cauchy
integral theorem
c appendix : characterizations of elementary domains

ⅴ elliptic functions
ⅴ.1 liouville's theorems
a appendix to the definition of the period lattice
ⅴ.2 the weierstrass -function
ⅴ.3 the field of elliptic functions
a appendix to sect. v.3 : the torus as an algebraic curve
ⅴ.4 the addition theorem
ⅴ.5 elliptic integrals
ⅴ.6 abel's theorem
ⅴ.7 the elliptic modular group
ⅴ.8 the modular function j

ⅵ elliptic modular forms
ⅵ.1 the modular group and its fundamental region
ⅵ.2 the k/12-formula and the injectivity　of the j-function
ⅵ.3 the algebra of modular forms
ⅵ.4 modular forms and theta series
ⅵ.5 modular forms for congruence groups
a appendix to v1.5 : the theta group
ⅵ.6 a ring of theta fhnctions

ⅶ　analytic number theory
ⅶ.1 sums of four and eight squares
ⅶ.2 dirichlerr series
ⅶ.3 dirichlet series with functional equations
ⅶ.4 the riemann <-function and prime numbers
ⅶ.5 the analytic continuation of the <-function
ⅶ.6 a tauberian theorem

ⅷ solutions to the exercises
ⅷ.1 solutions to the exercises of chapter ⅰ
ⅷ.2 solutions to the exercises of chapter ⅱ
ⅷ.3 solutions to the exercises of chapter ⅲ
ⅷ.4 solutions to the exercises of chapter ⅳ
ⅷ.5 solutions to the exercises of chapter ⅴ
ⅷ.6 solutions to the exercises of chapter ⅵ
ⅷ.7 solutions to the exercises of chapter ⅶ
r/eferences
symbolic notations

展开全部