| 書目名稱 | Number Theory | | 副標題 | Volume II: Analytic | | 編輯 | Henri Cohen | | 視頻video | http://file.papertrans.cn/669/668859/668859.mp4 | | 概述 | Unique collection of topics centered around a unifying topic.More than 350 exercises.Text is largely self-contained | | 叢書名稱 | Graduate Texts in Mathematics | | 圖書封面 |  | | 描述 | .The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. ..The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming .Volume I.. ..The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the | | 出版日期 | Textbook 2007 | | 關鍵詞 | algebra; diophantine equation; finite field; geometry; number theory | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-387-49894-2 | | isbn_softcover | 978-1-4419-2388-2 | | isbn_ebook | 978-0-387-49894-2Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer-Verlag New York 2007 |
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