Max Deuring

Max Deuring (9 December 1907 – 20 December 1984) was a German mathematician, who was elected a fellow of the Leopoldina.

Max Deuring in 1973

Quotes

• Since an algebraic function w(z) is defined implicitly by an equation of the form f(z,w) = 0, where f is a polynomial, it is understandable that the study of such functions should be possible by algebraic methods. Such methods also have the advantage that the theory can be developed in the most general setting, viz. over an arbitrary field, and not only over the field of complex numbers (the classical case).
• Lectures on the Theory of Algebraic Functions of One Variable. Lecture Notes in Mathematics. 314. Springer-Verlag. 1973. p. 1. 

Quotes about Deuring

• ... H. Hasse perceived the connection between complex multiplication and the Riemann hypothesis for congruence zeta functions, which was later proved by A. Weil in a fully general form. This observation led M. Deuring to establish a purely algebraic treatment of complex multiplication of elliptic curves. He could, moreover, along the same line of ideas, determine the zeta functions of elliptic curves with complex multiplication. The definition of zeta function of an algebraic curve defined over an algebraic number field is originally due to Hasse; and Weil is the first contributor to this subject.
  • Goro Shimura: Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)