商品描述
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The first is the local aspect, the second is the global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject, and embodies in a beautiful way the local and global aspects of Diophantine problems. This unique collection of topics contains more than 350 exercises and its text is largely self-contained.
商品描述(中文翻譯)
本書探討了現在所稱的「顯式數論」的幾個方面。其中心主題是解決丟番圖方程（Diophantine equations），即必須在整數、有理數或更一般的代數數中解決的方程或多項式方程組。這一主題，特別是，成為現代算術代數幾何理論的核心動機。在本書中，這一主題通過其三個最基本的方面來考量。第一個是局部方面，第二個是全球方面，第三個方面是ζ（zeta）和L（L）函數的理論。最後這一方面可以被視為整個主題的統一主題，並以美麗的方式體現了丟番圖問題的局部和全球方面。這個獨特的主題集合包含了超過350個練習題，其文本大部分是自足的。
