Introduction to Cyclotomic Fields
Introduction to Cyclotomic Fields
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DOI：
10.1007/978-1-4612-1934-7
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发表时间：
1982
影响因子：
4
通讯作者：
L. Washington
中科院分区：
文献类型：
--
作者：
L. Washington
介绍分圆领域是一个精心编写的阐述了一个中心领域的数论，可以作为第二课程代数数论。从一个初级水平开始，卷涵盖p进L-函数，类数，分圆单位，费马最后定理，和岩泽的理论Z_p-扩展，导致读者了解现代研究文献。包括许多练习。第二版包括一个新的章节，介绍塞恩、科利瓦金和鲁宾的工作，包括主要猜想的证明。还有一章给出了其他最近的发展，包括通过Jacobi和和Sinnott的消失岩泽的f-不变量的素数测试。
Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions, leading the reader to an understanding of modern research literature. Many exercises are included. The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.