Sergei Aleksandrovich Stepanov (Сергей Александрович Степанов; 24 February 1941) is a Russian mathematician, specializing in number theory. He is known for his 1969 proof using elementary methods of the Riemann hypothesis for zeta-functions of hyperelliptic curves over finite fields, first proved 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 one of the most influential mathematicians of the twentieth century. His influence is du ...
in 1940–1941 using sophisticated, deep methods in algebraic geometry.
Stepanov received in 1977 his Russian doctorate (higher doctoral degree) from the
Steklov Institute
Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Ste ...
under
Dmitry Konstantinovich Faddeev
Dmitry Konstantinovich Faddeev ( rus, Дми́трий Константи́нович Фадде́ев, , ˈdmʲitrʲɪj kənstɐnʲˈtʲinəvʲɪtɕ fɐˈdʲe(j)ɪf; 30 June 1907 – 20 October 1989) was a Soviet mathematician.
Biography
Dmitry w ...
with dissertation (translated title) ''An elementary method in algebraic number theory''. He was from 1987 to 2000 a professor at the Steklov Institute in Moscow.
[Steklov Mathematical Institute]
/ref> In the 1990s he was also at Bilkent University
Bilkent University () is a private non-profit research university located in Ankara, Turkey. It was founded by İhsan Doğramacı, the first president of the Council of Higher Education and the head of the prominent Doğramacı family, with th ...
in Ankara
Ankara is the capital city of Turkey and List of national capitals by area, the largest capital by area in the world. Located in the Central Anatolia Region, central part of Anatolia, the city has a population of 5,290,822 in its urban center ( ...
. He is at the Institute for Problems of Information Transmission of the Russian Academy of Sciences
The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...
.
Stepanov is best known for his work in arithmetic algebraic geometry, especially for the Weil conjectures
In mathematics, the Weil conjectures were highly influential proposals by . They led to a successful multi-decade program to prove them, in which many leading researchers developed the framework of modern algebraic geometry and number theory.
Th ...
on algebraic curves. He gave in 1969 an "elementary" (''i.e.'' using elementary methods) proof of a result first proved by André Weil using sophisticated methods, not readily understable by mathematicians who are not specialists in algebraic geometry. Wolfgang M. Schmidt
Wolfgang M. Schmidt (born 3 October 1933) is an Austrian mathematician working in the area of number theory. He studied mathematics at the University of Vienna, where he received his PhD, which was supervised by Edmund Hlawka, in 1955. Wolfgang ...
extended Stepanov's methods to prove the general result, and Enrico Bombieri
Enrico Bombieri (born 26 November 1940) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. Bombieri is currently professor emeritus in the School of Mathematics ...
succeeded in using the work of Stepanov and Schmidt to give a substantially simplified, elementary proof of the Riemann hypothesis for zeta-functions of curves over finite fields. Stepanov's research also deals with applications of algebraic geometry to coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...
.
He was an Invited Speaker of the ICM ICM may refer to:
Organizations
* Irish Church Missions, an Anglican mission
* Institut du Cerveau, the Paris Brain Institute, a research center
* Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw
* Interna ...
in 1974 in Vancouver. He received in 1975 the USSR State Prize
The USSR State Prize () was one of the Soviet Union’s highest civilian honours, awarded from its establishment in September 1966 until the dissolution of the USSR in 1991. It recognised outstanding contributions in the fields of science, mathem ...
.[ He was elected a Fellow of the ]American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
in 2012.
Selected publications
Codes on Algebraic Curves
Kluwer 1999
New York, Plenum Publishing 1994,
Number theory and its applications
Marcel Dekker 1999
References
External links
Stepanov at Mathnet.ru
{{DEFAULTSORT:Stepanov, Sergei
Recipients of the USSR State Prize
Russian mathematicians
Fellows of the American Mathematical Society
1941 births
Living people