Lectures on Elliptic Curves 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024


Lectures on Elliptic Curves

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J. W. S. Cassels 作者
Cambridge University Press
譯者
1991-11-21 出版日期
144 頁數
GBP 19.99 價格
Paperback
London Mathematical Society Student Texts 叢書系列
9780521425308 圖書編碼

Lectures on Elliptic Curves 在線電子書 圖書標籤: 橢圓麯綫  數論  數學  Cassels  on  Lectures  LMSST  Elliptic   


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Lectures on Elliptic Curves 在線電子書 epub 下載 mobi 下載 pdf 下載 txt 下載 2024

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Lectures on Elliptic Curves 在線電子書 pdf 下載 txt下載 epub 下載 mobi 下載 2024



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Lectures on Elliptic Curves 在線電子書 圖書描述

The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text.

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