From Classical L-Functions to Modern Reciprocity Laws
暫譯: 從古典 L-函數到現代互惠法則
Sorensen, Claus
- 出版商: Springer
- 出版日期: 2026-01-03
- 售價: $2,670
- 貴賓價: 9.5 折 $2,537
- 語言: 英文
- 頁數: 350
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 303203034X
- ISBN-13: 9783032030344
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相關分類:
離散數學 Discrete-mathematics
海外代購書籍(需單獨結帳)
相關主題
商品描述
The distinctive compilation of topics in this text provides readers with a smooth and leisurely transition from basic number theory to graduate topics courses on the Langlands program. It is a unique and self-contained resource for number theorists, instructors teaching basic analytic number theory, and the target readership of first and second year graduate students interested in number theory. Portions of the content are also accessible to mathematically mature advanced undergraduates. The copious number of exercises and examples throughout the text, aptly guide the reader. The prerequisite for using the book is a grounded understanding of number fields and local fields.
The book is well designed in its aims to build a bridge from beginning number theory topics to modern, advanced ones. Starting from scratch with the classical theory (Riemann's zeta function, Dirichlet L-functions, Dedekind zeta functions) it merges into a detailed account of Artin L-functions, Tate's thesis, and culminates in a discussion of the Deligne-Serre theorem and related results. These topics have not appeared together in book form.商品描述(中文翻譯)
這本書獨特的主題編排為讀者提供了一個從基本數論到研究生課程（Langlands計畫）的平滑且悠閒的過渡。它是數論學者、教授基本解析數論的教師，以及對數論感興趣的一、二年級研究生的獨特且自足的資源。部分內容對數學成熟的高年級本科生也同樣可及。書中大量的習題和範例恰如其分地指導讀者。使用本書的前提是對數域和局部域有扎實的理解。
這本書的設計目的是從初級數論主題建立一座通往現代高級主題的橋樑。從經典理論（黎曼ζ函數、狄利克雷L函數、德德金ζ函數）開始，逐漸融合進對阿廷L函數、塔特論文的詳細說明，並最終討論德利涅-塞爾定理及相關結果。這些主題在書籍形式中尚未同時出現過。
作者簡介
Claus Sorensen received his Ph.D. in Mathematics from the California Institute of Technology in 2006. Following graduation Sorensen was employed at Princeton University, first as an Instructor from 2006 to 2009, then as an Assistant Professor from 2009-2013. Professor Sorensen's main area of research is Number Theory and Representation Theory centering on the interaction between automorphic forms and Galois representations, commonly referred to as the Langlands program.
作者簡介(中文翻譯)
克勞斯·索倫森於2006年在加州理工學院獲得數學博士學位。畢業後，索倫森在普林斯頓大學工作，首先擔任講師，任期為2006年至2009年，然後於2009年至2013年擔任助理教授。索倫森教授的主要研究領域是數論和表示論，專注於自同態形式與伽羅瓦表示之間的互動，通常稱為朗蘭茲計畫。
