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Emil Artin and beyond—class field theory and L-functions

Tác giả: Della Dumbaugh , Joachim Schwermer
Loại tài liệu: Sách, chuyên khảo, tuyển tập
Ký hiệu: Lv7313
Mã giá: 01DU
Nội dung tóm tắt: Xem chi tiết
This book explores the development of number theory, and class field theory in particular, as it passed through the hands of Emil Artin, Claude Chevalley and Robert Langlands in the middle of the twentieth century. Claude Chevalley’s presence in Artin’s 1931 Hamburg lectures on class field theory serves as the starting point for this volume. From there, it is traced how class field theory advanced in the 1930s and how Artin’s contributions influenced other mathematicians at the time and in subsequent years. Given the difficult political climate and his forced emigration as it were, the question of how Artin created a life in America within the existing institutional framework, and especially of how he continued his education of and close connection with graduate students, is considered. In particular, Artin’s collaboration in algebraic number theory with George Whaples and his student Margaret Matchett’s thesis work “On the zeta-function for ideles” in the 1940s are investigated. A (first) study of the influence of Artin on present day work on a non-abelian class field theory finishes the book. The volume consists of individual essays by the authors and two contributors, James Cogdell and Robert Langlands, and contains relevant archival material. Among these, the letter from Chevalley to Helmut Hasse in 1935 is included, where he introduces the notion of ideles and explores their significance, along with the previously unpublished thesis by Matchett and the seminal letter of Langlands to André Weil of 1967 where he lays out his ideas regarding a non-abelian class field theory. Taken together, these chapters offer a view of both the life of Artin in the 1930s and 1940s and the development of class field theory at that time. They also provide insight into the transmission of mathematical ideas, the careful steps required to preserve a life in mathematics at a difficult moment in history, and the interplay between mathematics and politics (in more ways than one). Some of the technical points in this volume require a sophisticated understanding of algebra and number theory. The broader topics, however, will appeal to a wider audience that extends beyond mathematicians and historians of mathematics to include historically minded individuals, particularly those with an interest in the time period
Mục lục: Xem chi tiết
I. Class field theory: From Artin’s course in Hamburg to Chevalley’s “Éléments idéaux” II. Creating a life: Emil Artin in America III. The collaboration of Emil Artin and George Whaples IV. Margaret Matchett: Artin’s student at Indiana and her thesis V. L-functions VI. Automorphic L-functions

Thông tin chi tiết

    Dạng tài liệu:Bản in
    Chỉ số ISBN:978-3-03719-146-0,
    Nguồn: Tặng biếu : Prof. Phan Thành An tặng
    Mã giá:01DU
    Mã MSC:01A60 , 01A70 , 11M06
    Tác giả:Della Dumbaugh, Joachim Schwermer
    Nhan đề:Emil Artin and beyond—class field theory and L-functions
    Số trang: 244
    Từ Khóa:class field theory , Emil Artin
    Bộ sách:Heritage of European Mathematics

Thông tin xếp giá

  • ĐKCB: Lv7313
  • Tổng số bản: 1
  • Tổng số bản rỗi: 0
  • Tổng số đang đặt chỗ: 0

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