Number Theory
Number Theory
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DOI：
10.1007/978-3-642-66671-1
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发表时间：
1979-12
期刊：
影响因子：
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通讯作者：
Helmut Hasse
中科院分区：
文献类型：
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作者：
Helmut Hasse
尽管事实上，现在有相当多的书籍代数数论提供给数学界，似乎仍然是一个强烈需要一个基本的工作，如哈塞的“Zahlentheorie”。这种印象是证实了大量的询问编辑收到的日期出现的英文翻译哈塞的书。一个主要原因是不断的兴趣在这本书可能在于其生动的介绍divisortheorical方法代数数论，一种方法是发达国家的哈塞的前教师亨泽尔和进一步扩大哈塞本人。哈塞并不满足于仅仅介绍数论材料，而是激发了基本思想和问题，对它们进行了详细的评论，并指出了它们与邻近数学分支的联系。在准备哈塞的《数论》的英文版时，我试图尽可能地保留这本书的独特风格和特点，即使冒着使用部分不足或有些笨拙的英语的风险。特别是，我保留了这本书的原始符号，从而遵循Hasse规定的要求。这意味着，例如，表示环的合理整数，P领域的有理数，P∞领域的真实的数字，P，p-adic完成的P，和Zo领域的复数。[8]本书的英文译本是在德文《Zahlentheorie》第三版的基础上编写的。与德文版相比，只有一个主要的变化：第16章不得不大部分重写，以删除JB Leicht和P. Roquette发现并纠正的错误。这是由JB Leicht完成的重写，我感谢他对本书的贡献。除了这一变化，只有一些小错误已被删除，一些新的参考书目已被添加，并在表和计算书的最后几个更新已被纳入。感谢F。Halter-Koch和HW Lenstra Jr.他向我指出了德文版中的一些错误，并向A. Odlyzko关于判别式估计的建议。我非常感激B。戈登谁采取的麻烦仔细阅读英文手稿，并提出了大量的改进文体和数学性质。最后但并非最不重要的是，我也想感谢我尊敬的前老师哈塞教授，他对我在编辑和准备这本书方面的缓慢进展给予了耐心。
In spite of the fact that nowadays there are quite a few books on algebraic number theory available to the mathematical community, there seems to be still a strong need for a fundamental work like Hasse's „Zahlentheorie". This impression is corroborated by the great number of inquiries the editor received about the date of appearance of the English translation of Hasse's book. One main reason for the unbroken interest in this book lies probably in its vivid presentation of the divisortheoretic approach to algebraic number theory, an approach which was developed by Hasse's former teacher Hensel and further expanded by Hasse himself. Hasse does not content himself with a mere presentation of the number-theoretic mate-rial, but he motivates the basic ideas and questions, comments on them in detail, and points out their connections with neighboring branches of mathematics. In preparing the English edition of Hasse's" Number Theory", I tried to preserve as much as possible the unique style and features of the book, even at the risk of using a partly insufficient or somewhat clumsy English. In particular, I kept the original notation of the book thus following the requirements stipulated by Hasse. This means, eg, that denotes the ring of rational integers, P the field of rational numbers, P∞ the field of real numbers, P, the p-adic completion of P, and Zo the field of complex numbers. 8 The present English translation of the book was prepared on the basis of the third edition of the German, Zahlentheorie". Only one major change from the German edition was made: Chapter 16 had to be largely rewritten in order to remove an error detected and corrected by JB Leicht and P. Roquette. This rewriting has been done by JB Leicht to whom I owe thanks for this contribu-tion to the book. Besides that change, only some minor errors have been eliminated, some new bibliographical references have been added, and a few updatings in the tables and computations at the end of the book have been incorporated. Thanks are due to F. Halter-Koch and HW Lenstra jr. for pointing out to me some errors in the German edition, and to A. Odlyzko for his advice regarding estimates of discriminants. I am deeply indebted to B. Gordon who took the trouble of carefully reading the English manuscript and suggesting lots of improvements of a stylistic and mathematical nature. Last but not least I also wish to thank my esteemed former teacher Professor Hasse for his patience with my slow progress in editing and preparing this book.