Peter Roquette

In 1951 he defended a dissertation at the University of Hamburg under Helmut Hasse, providing a new proof of the Riemann hypothesis for algebraic function fields over a finite field (the first proof was given by André Weil in 1940).

He applied the methods of model theory (nonstandard arithmetic) in number theory, joint with Abraham Robinson, with whom he worked on Mahler's theorem (on the finiteness of integral points on a curve of genus g > 0) using non-standard methods.

He authored a number of works on the history of mathematics, in particular on the schools of Helmut Hasse and Emmy Noether.

In 1958 he was an invited speaker at the International Congress of Mathematicians in Edinburgh (on the topic of "Some fundamental theorems on abelian function fields").

His doctoral students include Gerhard Frey and Volker Weispfenning [de].