Martin Čech: Moments of real Dirichlet L-functions and multiple Dirichlet series

Abstract:

 There are two common approaches to tackle moments of L-functions: either approximations by Dirichlet polynomials, or using multiple Dirichlet series. The second approach is usually based on modifying the multiple Dirichlet series into a “perfect” object, which satisfies certain functional equations. During this talk, we will relate the two approaches and introduce a way to work with the multiple Dirichlet series without modifying it, which leads to a simpler and more natural computations of the moments. More specifically, we prove an explicit region of meromorphic continuation of the multiple Dirichlet series associated with moments of real Dirichlet L-functions, which will be wide enough to give the first 3 moments with power-saving error term.