Lethbridge Number Theory and Combinatorics Seminar: Kirsty Chalker

Previously, in this seminar series, we have heard about explicit bounds on the sum of values of the von Mangoldt function Lambda(n) (for n x). The point of lift-off for bounding this sum is the explicit formula, which pulls the zeros of the Riemann zeta-function into the equation. However, there are other sums for which using an explicit formula is currently unconditionally impossible. In this talk, I will outline the work of my current thesis, in which I prove bounds for the sum of a somewhat general function a_n/n^s where a_n and s are complex numbers, and apply these bounds to the sums of mu(n) and mu(n)/n, which refer to the Mobius function mu(n).