| 書目名稱 | Number Theory in Function Fields | | 編輯 | Michael Rosen | | 視頻video | http://file.papertrans.cn/669/668882/668882.mp4 | | 概述 | Includes supplementary material: | | 叢書名稱 | Graduate Texts in Mathematics | | 圖書封面 |  | | 描述 | Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson‘s theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet‘s theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con- sidering finite algebraic extensions K of Q, which are called algeb | | 出版日期 | Textbook 2002 | | 關(guān)鍵詞 | Algebraic Function Fields; Algebraic Geometry; Function Fields; Number theory; Prime; Prime number; finite | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4757-6046-0 | | isbn_softcover | 978-1-4419-2954-9 | | isbn_ebook | 978-1-4757-6046-0Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 2002 |
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