Beijing-Moscow Mathematics Colloquium (online)
Abstract
Additive Divisor Problem (ADP) is concerned with finding an asymptotic formula for the sum $\sum_{n<X}d(n)d(n+a)$, where $d(n)=\sum_{d|n}1$ is the divisor function. Surprisingly, the ADP arises naturally in quite different problems of number theory. For example, it is related to the investigation of the 4th moment of the Riemann zeta-function, the second moment of automorphic $L$-functions and the mean values of the length of continued fractions. In the talk, I will describe the ADP and its applications.
Bio
Dmitry Frolenkov received his PhD degree from Steklov Mathematical Institute in 2013. Starting from 2014 he works at Steklov Mathematical Institute as a senior researcher. Besides he got the RAS award for young scientists of Russia. His research interests are centered around an analytic number theory with a special emphasis on the theory of L-functions associated to automorphic forms.
