Forgive me for my ignorance, but I'm very surprised to learn that there are two Vinogradovs, both famous in the field of analytic number theory. Guessing from their names and the Russian naming convention, is one the son of the other?
The answer seems to be no. It is hard to find direct confirmation, but every time their names are mentioned together it is made clear that there's no relationship.
The Russian mathematician Askold Ivanovich Vinogradov is not to be confused with the other Russian mathematician (the mathematical great-grandchild of Pafnuty Lvovich Chebyshev) whose work is at the heart of this paper: Ivan Matveyevich Vinogradov.
(Newsletter of the European Mathematical Society, issue 90)
There is a theorem due to Askold Ivanovich Vinogradov (1929-2005, not to be confused with another and more famous Russian mathematician, Ivan Matveevich Vinogradov, 1891-1988) that states...
Ian Hacking, Why Is There Philosophy of Mathematics At All?
In this obituary in the Russian Mathematical Surveys there's also no mention of him having children, let alone another somewhat famous soviet mathematician.
Ivan Matveyevich Vinogradov's Wikipedia article also mentions that he never married.