割圆域导论-第2版

作者：华盛顿

页数：487

出版社：世界图书出版公司

出版日期：2014

ISBN：9787510077852

电子书格式：pdf/epub/txt

内容简介

华盛顿所著的《割圆域导论（第2版）（英文版）》是一部讲述数论很重要领域的教程，包括p进数L—函数、类数、割圆单元、费马最后定理和Z—p扩展Iwasawa定理。这是第二版，新增加了许多内容，如Thaine，Kolyvagin，andRubin的著作、主猜想的证明，以及一章最新其他进展。目次：费曼大定理；基本结果；狄里克莱性质；狄里克莱L级数和类数公式；p进数和伯努利数；Stickelberger定理；p进数L—函数的Iwasawa结构；割圆单元；费曼大定理第二案例；伽罗瓦群作用于理想类群上；类数1的割圆域；测度与分布。

作者简介

Lawrence C. Washington(L.C.华盛顿,美国)是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。

本书特色

　　since the publication of the first edition， several
remarkable developments have taken place. the work of thaine， kolyvagin， and
rubin has produced fairly elementary proofs of ribet’s converse of herbrand’s
theorem and of the main conjecture. the original proofs of both of these results
used delicate techniques from algebraic geometry and were inaccessible to many
readers. also， sinnott discovered a beautiful proof of the vanishing of
iwasawa’s u-invariant that is much simpler than the one given in chapter 7.
finally， fermat’s last theorem was proved by wiles， using work of frey， ribet，
serre， mazur， langlands-tunnell， taylor-wiles， and others. although the proof，
which is based on modular forms and elliptic curves， is much different from the
cyclotomic approaches described in this book， several of the ingredients were
inspired by ideas from cyclotomic fields and iwasawa theory. 

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