Roquette was born in
Königsberg on 8 October 1927. He studied in
Erlangen,
Berlin, and
Hamburg. 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). In 1951/1952 he was an assistant at the Mathematical Research Institute at
Oberwolfach and from 1952 to 1954 at the
University of Munich. From 1954 to 1956 he worked at the
Institute for Advanced Study in Princeton. In 1954 he was Privatdozent at Munich, and from 1956 to 1959 he worked in the same position at Hamburg. In 1959 he became an associate professor at the
University of Saarbrucken and in the same year at the
University of Tübingen. From 1967 he was professor at the
Ruprecht-Karls-University of Heidelberg, where he retired in 1996. Roquette worked on
number and function fields and especially local
p-adic fields. 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 1975 Roquette was co-editor of the collected essays by Helmut Hasse. From 1978, Roquette was a member of the
Heidelberg Academy of Sciences and from 1985, the
German Academy of Sciences Leopoldina. He has an honorary doctorate from the
University of Duisburg-Essen and was an honorary member of the
Mathematical Society of Hamburg. 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 . Roquette died in
Heidelberg on 24 February 2023, at the age of 95. ==Selected publications==