Video library: M. A. Korolev, Incomplete Kloosterman sums and solvability of some congruences with prime variables

VIDEO LIBRARY


Мemorial conference dedicated to the memory of Ivan Matveevich Vinogradov March 28, 2019 15:30, Moscow, Steklov Mathematical Institute, Conference hall

Incomplete Kloosterman sums and solvability of some congruences with prime variables M. A. Korolev^ab ^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow ^b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract: The talk is devoted to a new estimate for a special incomplete Kloosterman sum and its applications to the problems of the solvability of some congruences modulo $q$. The variables in these congruences run through prime numbers lying in the short interval of the type $(1,N]$, where $N\ll q^{1-c}$, $c>0$.