数论 下载 mobi epub pdf 电子书 2024

☆☆☆☆☆
简体网页||繁体网页



点击这里下载

类似图书 点击查看全场最低价

---

内容简介

In spite of the fact that nowadays there are quite a few books on algebraic number theory available to the mathematical community, there seems to be still a strong need for a fundamental work like IIasse's ,,Zahlentheorie". This impression is corroborated by the great number of inquiries the editor received about the date of appearance of the English translation of Hasse's book. One main reason for the unbroken interest in this book lies probably in its vivid presentation of the divisortheoretic approach to algebraic number theory, an approach which was developed by Hasse's former teacher IIensel and further expanded by Hasse himseff. Hasse does not content himself with a mere presentation of the number-theoretic material, but he motivates the basic ideas and questions, comments on them in detail,and points out their connections with neighboring branches of mathematics.

目录

part ⅰ. the foundations of arithmetic in the rational number field
chapter 1. prime decomposition
function fields
chapter 2. divisibility
function fields
chapter 3. congruences
function fields
the theory of finite fields
chapter 4. the structure of the residue class ring mod m and of the reduced residue class group mod m
1. general facts concerning direct products and direct sums
2. direct decomposition of the residue class ring mod m and of the reduced residue class group mod m
3. the structure of the additive group of the residue class ring mod m
4. on the structure of the residue class ring mod pμ
5. the structure of the reduced residue class group mod pμ
function fields
chapter 5. quadratic residues
1. theory of the characters of a finite abelian group
2. residue class characters and numerical characters mod m
3. the basic facts concerning quadratic residues
4. the quadratic reciprocity law for the legendre symbol
5. the quadratic reciprocity law for the jacobi symbol
6. the quadratic reciprocity law as product formula for the hilbcrt symbol
7. special cases of dirichlet's theorem on prime numbers in reduced residue classes
function field

part ⅱ. the theory of valued fields
chapter 6. the fundamental concepts regarding valuations
1. the definition of a valuation； equivalent valuations
2. approximation independence and multiplicative independence of valuations
3. valuations of the prime field
4. value groups and residue class fields
function fields
chapter 7. arithmetic in a discrete valued field
divisors from an ideal-theoretic standpoint
chapter 8. the completion of a valued field
chapter 9. the completion of a discrete valued field. the lo-adie number fields
function fields
chapter 10. the isomorphism types of complete discrete valued fields with perfect residue class field
1. the multiplicative residue system in the case of prime characteristic
2. the equal-characteristic case with prime characteristic
3. the multiplicative residue system in the p-adic number field
4. witt's vector calculus
5. construction of the general p-adic field
6. the unequal-characteristic case
7. isomorphic residue systems in the case of characteristic 0
8. the isomorphic residue systems for a rational function field
9. the equal-characteristic case with characteristic 0
chapter 11. prolongation of a discrete valuation to a purely transcendental extension
chapter 12. prolongation of the valuation of a complete field to a finitealgebraic extension
1. the proof of existence
2. the proof of completeness
3. the proof of uniqueness
chapter 13. the isomorphism types of complete archimedean valued fields
chapter 14. the structure of a finite-algebraic extension of a complete discrete valued field
1. embedding of the arithmetic
2. the totally ramified case
3. the unramified case with perfect residue class field
4. the general case with perfect residue class field
5. the general case with finite residue class field
chapter 15. the structure of the multiplicative group of a complete discrete valued field with perfect residue class field of prime characteristic
1. reduction to the one-unit group and its fundamental chain of subgroups
2. the one-unit group as an abelian operator group
3. the field of nth roots of unity over a p-adic number field
4. the structure of the one-unit group in the equal-charaeteristie case with finite residue class field
5. the structure of the one-unit group in the p-adie case
6. construction of a system of fundamental one-units in the p-adic case
7. the one-unit group for special p-adic number fields
8. comparison of the basis representation of the multiplieative group in the p-adic case and the archimedean case
chapter 16. the tamely ramified extension types of a complete discrete valued field with finite residue class field of characteristic p
chapter 17. the exponential function， the logarithm， and powers in a complete non-archimedean valued field of characteristic 0
1. integral power series in one indeterminate over an arbitrary field
2. integral power series in one variable in a complete non-archimedean valued field
3. convergence
4. functional equations and mutual relations
5. the discrete case
6. the equal-characteristic case with characteristic 0
chapter 18. prolongation of the valuation of a non-complete field to a finite-algebraic extension
1. representations of a separable finite-algebraic extension over an arbitrary extension of the ground field
2. the ring extension of a separable finite-algebraic extension by an arbitrary ground field extension， or the tensor product
of the two field extensions
3. the characteristic polynomial
4. supplements for inseparable extensions
5. prolongation of a valuation
6. the discrete case
7. the archimedean case

part ⅲ. the foundations of arithmetic in algebraic number fields
chapter 19. relations ]3etween the complete system of valuations and the arithmetic of the rational number field
1. finiteness properties
2. characterizations in divisibility theory
3. the product formula for valuations
4. the sum formula for the principal parts function fields
the automorphisms of a rational function field
chapter 20. prolongation of the complete system of valuations to a finitealgebraic extension
function fields
concluding remarks
chapter 21. the prime spots of an algebraic number field and their completions
function fields
chapter 22. decomposition into prime divisors， integrality， and divisibility
1. the canonical homomorphism of the multiplicative group into the divisor group
2. embedding of divisibility theory under a finite-algebraic extension
3. algebraic characterization of integral algebraic numbers
4. quotient representation
function fields
constant fields， constant extensions
chapter 23. congruences
1. ordinary congruence
2. multiplicative congruence
function fields
chapter 24. the multiples of a divisor
1. field bases
2. the ideal property， ideal bases
3. congruences for integral elements
4. divisors from the ideal-theoretic standpoint
5. further remarks concerning divisors and ideals
function fields
constant fields for p. characterization of prime divisors by homomorphisms. decomposition law under an algebraic constant extension
the rank of the module of multiples of a divisor
chapter 25. differents and discriminants
1. composition formula for the trace and norm. the divisor trace
2. definition of the different and diseriminant
3. theorems on differents and discriminants in the small
4. the relationship between differents and discriminants in the small and in the large
5. theorems on differents and discriminants in the large
6. common inessential discriminant divisors
7. examples
function fields
the number of first-degree prime divisors in the case of a finite constant field
differentials
the riemann-roch theorem and its consequences
disclosed algebraic function fields
chapter 26. quadratic number fields
1. generation in the large and in the small
2. the decomposition law
3. discriminants， integral bases
4. quadratic residue characters of the discriminant of an arbitrary algebraic number field
5. the quadratic number fields as class fields
6. the hilbert symbol as norm symbol
7. the norm theorem
8. a necessary condition for principal divisors. genera
chapter 27. cyelotomic fields
1. generation
2. the decomposition law
3. discriminants， integral bases
4. the quadratic number f 数论 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

好，我十分满意。我太满意了。哈哈哈哈

评分☆☆☆☆☆

帮人买的。他说不错，那就不错吧

评分☆☆☆☆☆

不错吧，物流还是有点坑

评分☆☆☆☆☆

好，我十分满意。我太满意了。哈哈哈哈

评分☆☆☆☆☆

Springer的书必属经典

评分☆☆☆☆☆

只想说几个字，好书，好书，好书，还很厚，内容丰富。

评分☆☆☆☆☆

好，我十分满意。我太满意了。哈哈哈哈

评分☆☆☆☆☆

GTM的系列都是经典啊，Graduate Texts in Mathematics，这是一个数学基础系列书籍，包括了林林总总各大小分支的数学教材，适用人群为本科生中的有志青年和研究生们

评分☆☆☆☆☆

一个老是受班上同学欺负的瘦弱小男孩，因为拥有一种特殊能力而强大：他能“ 偷别人的影子” ，因而能看见他人心事，听见人们心中不愿意说出口的秘密。他开始成为需要帮助者的心灵伙伴，为每个偷来的影子点亮生命的小小光芒。[1] 某年灿烂的夏天，他在海边邂逅一位又聋又哑的女孩。他该如何用自己的能力帮助她？他将如何信守与她共许的承诺？[2] [3]不知道姓氏的克蕾儿。一个会用风筝写出“我想你”的女孩啊，让人永远都忘不了。[3] 一段缠绵多年的爱恋，一段进行中的不完美爱情。故事温柔风趣，轻盈优雅，能让你我真正感受到心跳的爱情疗愈小说。一个爱与友情盛开的美丽世界，在此，想象力超越了一切日常生活及人际关系。一本关于童年追忆、关于深藏在成年人内心深处梦想的小说。马克．李维一贯的写作风格，国外出版社定义本书为“温柔又风趣”。容易贴近台湾女性读者的心。有浪漫的爱情元素、父母亲子课题、朋友相挺的义气，迎合大众市场。爱情场景刻画细致，对白浪漫感人，尤其结局会让女性感动。母子亲情的刻画很催泪。跟《那些我们没谈过的事》写法相似，有不美满家庭长大的主角、有贴心好友、一段多年的爱恋、一段进行中的不完美爱情……最后，多年的情人浪漫复合。 2作品目录 楔子 001·我的童年就在那里，带点忧愁又有点悲痛，在这外省的小城市里，我拼命等着伊丽莎白垂怜而看我一眼，在绝望中等待长大。影子的秘密 005·为每一个你所偷来的影子找到点亮生命的小小光芒，为它们找回隐匿的记忆拼图，这便是我们对你的全部请托。海滩上的克蕾儿 071·她凝视着我，漾出一朵微笑，并且在纸上写下：“你偷走了我的影子，不论你在哪里，我都会一直想着你。” 吕克的梦想 089·生命中某些珍贵的片刻，其实都来自于一些微不足道的小事。如果我今晚没有留下来，我想我永远不会与母亲有此番深谈。与母亲一起离开阁楼后，我最后一次踱回天窗底下，默默感谢我的影子。苏菲的伤 131·我只是你生活里的一个影子，你却在我的生命里占有重要地位。如果我只是个单纯的过客，为何要让我闯入你的生活?我千百次想过要离开你，但仅凭一己之力我做不到。 偷影子的人被唤回的记忆 173·不知道姓氏的克蕾儿。这就是你在我生命里的角色，我童年时的小女孩，今日蜕变成了女人，一段青梅竹马的回忆，一个时间之神没有应允的愿望。用风筝写下的思念 201·一个会用风筝向你写出“我想你”的女孩啊，真让人永远都忘不了她。致谢 / 221 他们眼中《偷影子的人》/ 224 3点评鉴赏 《偷影子的人》是马克·李维的第10部作品，该书在法国首印45万册，位列全年销量排行榜的总冠军，法国媒体惊叹：“销售得比影子消失的速度还快！”这部作品完美展现了马克·李维温柔风趣的写作风格，有催人泪下的亲情、浪漫感人的爱情和不离不弃的友情，清新浪漫的气息和温柔感人的故事相互交织，带给读者笑中带泪的阅读感受，是一部唤醒童年回忆和内心梦想的温情疗愈小说。

类似图书 点击查看全场最低价