![Peter Roquette](https://upload.wikimedia.org/wikipedia/commons/4/47/Peter_Roquette.jpeg)
Peter Roquette (born 8 October 1927) is a German mathematician working in
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
,
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
, and
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
. He was born in
Königsberg
Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...
.
Roquette studied in
Erlangen
Erlangen (; East Franconian German, East Franconian: ''Erlang'', Bavarian language, Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative d ...
,
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
, and
Hamburg
(male), (female) en, Hamburger(s),
Hamburgian(s)
, timezone1 = Central (CET)
, utc_offset1 = +1
, timezone1_DST = Central (CEST)
, utc_offset1_DST = +2
, postal ...
. In 1951 he defended a dissertation at the
University of Hamburg
The University of Hamburg (german: link=no, Universität Hamburg, also referred to as UHH) is a public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('' Allgemeines Vor ...
under
Helmut Hasse
Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ...
, providing a new proof of the
Riemann hypothesis
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in ...
for
algebraic function field
In mathematics, an algebraic function field (often abbreviated as function field) of ''n'' variables over a field ''k'' is a finitely generated field extension ''K''/''k'' which has transcendence degree ''n'' over ''k''. Equivalently, an algebraic ...
s over a
finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...
(the first proof was given by
André Weil
André Weil (; ; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry. He was a founding member and the ''de facto'' early leader of the mathematical Bourbaki group. Th ...
in 1940). In 1951/1952 he was an assistant at the Mathematical Research Institute at
Oberwolfach
Oberwolfach ( gsw, label= Low Alemannic, Obberwolfä) is a town in the district of Ortenau in Baden-Württemberg, Germany. It is the site of the Oberwolfach Research Institute for Mathematics, or Mathematisches Forschungsinstitut Oberwolfach.
Ge ...
and from 1952 to 1954 at the
University of Munich
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's List of universities in Germany, sixth-oldest u ...
. From 1954 to 1956 he worked at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
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
Saarland University (german: Universität des Saarlandes, ) is a public research university located in Saarbrücken, the capital of the German state of Saarland. It was founded in 1948 in Homburg in co-operation with France and is organized in si ...
and in the same year at the
University of Tübingen
The University of Tübingen, officially the Eberhard Karl University of Tübingen (german: Eberhard Karls Universität Tübingen; la, Universitas Eberhardina Carolina), is a public research university located in the city of Tübingen, Baden-Wü ...
. From 1967 he was professor at the
Ruprecht-Karls-University
}
Heidelberg University, officially the Ruprecht Karl University of Heidelberg, (german: Ruprecht-Karls-Universität Heidelberg; la, Universitas Ruperto Carola Heidelbergensis) is a public research university in Heidelberg, Baden-Württemberg, ...
of Heidelberg, where he retired in 1996.
Roquette worked on
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
and function fields and especially local
''p''-adic fields. He applied the methods of
model theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...
(
nonstandard arithmetic) in number theory, joint with
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorpo ...
, with whom he worked on
Mahler's theorem
In mathematics, Mahler's theorem, introduced by , expresses continuous ''p''-adic functions in terms of polynomials. Over any field of characteristic 0, one has the following result:
Let (\Delta f)(x)=f(x+1)-f(x) be the forward difference operat ...
(on the finiteness of integral points on a curve of genus ''g'' > 0) using
non-standard
Standardization or standardisation is the process of implementing and developing technical standards based on the consensus of different parties that include firms, users, interest groups, standards organizations and governments. Standardization ...
methods. He authored a number of works on the
history of mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
, in particular on the schools of
Helmut Hasse
Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and ...
and
Emmy Noether
Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe ...
. In 1975 Roquette was co-editor of the collected essays by Helmut Hasse.
Since 1978 Roquette is member of the
Heidelberg Academy of Sciences
The Heidelberg Academy of Sciences and Humanities (German: ''Heidelberger Akademie der Wissenschaften''), established in 1909 in Heidelberg, Germany, is an assembly of scholars and scientists in the German state of Baden-Wuerttemberg.
The Academ ...
and since 1985, the
German Academy of Sciences Leopoldina
The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded ...
. He has an honorary doctorate from the
University of Duisburg-Essen
The University of Duisburg-Essen (german: link=no, Universität Duisburg-Essen) is a public research university in North Rhine-Westphalia, Germany. In the 2019 ''Times Higher Education World University Rankings'', the university was awarded ...
and is honorary member of the
Mathematical Society of Hamburg. In 1958 he was an
invited speaker at the International Congress of Mathematicians
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...
in
Edinburgh
Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...
(on the topic of "Some fundamental theorems on abelian function fields").
His doctoral students include
Gerhard Frey
Gerhard Frey (; born 1 June 1944) is a German mathematician, known for his work in number theory. Following an original idea of Hellegouarch, he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a pur ...
and .
Selected publications
* Analytic theory of elliptic functions over local fields. Vandenhoeck and Ruprecht 1970.
* With Franz Lemmermeyer (Editor): The Correspondence of Helmut Hasse and Emmy Noether 1925-1935 Göttingen State and University Library, 2006..
* with Günther Frei (Editor)
Emil Artin and Helmut Hasse - correspondence 1923-1934 University of Göttingen Publisher 2008
* The Brauer-Hasse-Noether Theorem in Historical Perspective. Mathem. the-Naturwiss writings. Class of the Heidelberg Academy of Sciences, Springer-Verlag, 2005.
* Anthony V. Geramita, Paulo Ribenboim (ed.): Collected Papers of Peter Roquette 3 volumes. Queens Papers in Pure and Applied Mathematics Bd.118, Kingston, Ontario, Queen's University, 2002.
* With Alexander Prestel: Formally p-adic Fields. Lecture Notes in Mathematics, Springer-Verlag 1984.
* Robinson, A.; Roquette, P. On the finiteness theorem of Siegel and Mahler concerning Diophantine equations. J. Number Theory 7 (1975), 121–176.
External links
*
homepage*
{{DEFAULTSORT:Roquette, Peter
1927 births
Possibly living people
20th-century German mathematicians
21st-century German mathematicians
University of Hamburg alumni
Academic staff of the Ludwig Maximilian University of Munich
Academic staff of Saarland University
Academic staff of the University of Tübingen
Academic staff of Heidelberg University
Number theorists
Model theorists
German historians of mathematics