Selberg’s shifted convolutions, multiple Dirichlet series and second moments of L-functions

Selberg’s shifted convolution was introduced by Selberg in 1965 and since then it has been recognized that its analytic properties play a very important role in several problems in analytic number theory. Recently, Hoffstein and his student Hulse defined a variant of Selberg’s convolutions in one and two variables and obtained their meromorphic continuations. In this talk, I will explain an application to second moment problems for GL(2) L-series. This is a joint work with Jeff Hoffstein.