# Emil Artin and Beyond—Class Field Theory and \(L\)-Functions

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*Della Dumbaugh; Joachim Schwermer*

A publication of the European Mathematical Society

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.

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 Claude
Chevalley to Helmut Hasse in 1935 is included, in which he introduces
the notion of ideles and explores their significance, along with the
previously unpublished thesis by Margaret Matchett and the seminal
letter of Robert Langlands to André Weil of 1967 in which 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in number theory and \(L\)-functions.