Sergei Vladimirovich Vostokov (; 13 April 1945 – 7 March 2025) was a Russian mathematician who made major contributions to
local number theory. He was a professor at
St. Petersburg State University.
Life and work
Vostokov developed an important class of explicit formulas for the
Hilbert symbol In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from ''K''× × ''K''× to the group of ''n''th roots of unity in a local field ''K'' such as the fields of real number, reals or p-adic numbers. It is related to rec ...
on
local fields, which had a wide range of applications in
number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
.
His formulas generalize to formal groups. A generalization of his explicit formula to higher local fields is called the
Vostokov symbol. It plays an important role in higher local
class field theory
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field.
Hilbert is credit ...
.
Vostokov died on 7 March 2025, at the age of 79.
Awards
For his 60th birthday, two special volumes of
St Petersburg Mathematical Society of Vostokov were published in Russian and English by 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 2014, Vostokov was awarded the Chebyshev Prize.
Bibliography
Books
*
References
External links
*
{{DEFAULTSORT:Vostokov, Sergei
1945 births
2025 deaths
Russian mathematicians
Saint Petersburg State University alumni
Academic staff of Saint Petersburg State University
Scientists from Saint Petersburg