Emil Artin and Beyond: Class Field Theory and L-functions

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.