| 書(shū)目名稱(chēng) | Quadratic Number Fields | | 編輯 | Franz Lemmermeyer | | 視頻video | http://file.papertrans.cn/781/780052/780052.mp4 | | 概述 | Connects quadratic fields with modern algebraic number theory.Applies the theory to solve Diophantine equations.Contains hundreds of exercises with solutions.Includes original historical commentary | | 叢書(shū)名稱(chēng) | Springer Undergraduate Mathematics Series | | 圖書(shū)封面 |  | | 描述 | This undergraduate textbook provides an elegant introduction to the arithmetic of quadratic number fields, including many topics not usually covered in books at this level. .Quadratic fields offer an introduction to algebraic number theory and some of its central objects: rings of integers, the unit group, ideals and the ideal class group. This textbook provides solid grounding for further study by placing the subject within the greater context of modern algebraic number theory. Going beyond what is usually covered at this level, the book introduces the notion of modularity in the context of quadratic reciprocity, explores the close links between number theory and geometry via Pell conics, and presents applications to Diophantine equations such as the Fermat and Catalan equations as well as elliptic curves. Throughout, the book contains extensive historical comments, numerous exercises (with solutions), and pointers to further study...Assuming a moderate background in elementary number theory and abstract algebra, .Quadratic Number Fields. offers an engaging first course in algebraic number theory, suitable for upper undergraduate students.. | | 出版日期 | Textbook 2021 | | 關(guān)鍵詞 | quadratic fields; Pell equation; class group; Gauss sum; Pell conics; modularity; Fermat‘s last theorem; Ca | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-78652-6 | | isbn_softcover | 978-3-030-78651-9 | | isbn_ebook | 978-3-030-78652-6Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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