He made major contributions to local number theory.
Vostokov developed an important class of explicit formulas for the Hilbert symbol on local fields, which have a wide range of applications in number theory.
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.
[2][failed verification] 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.