# Seminar

Speaker(s):
Let $\rho=\sigma+ i\gamma$  be a zero of the Riemann zeta function. The Landau-Gonek formula asserts that  $\sum_{0< \gamma< T} x^{\rho} = -\frac{T}{2\pi}\Lambda(x) + O(\log T).$
where $\Lambda(x) = \log p$ if  $x=p^i$ and $\Lambda(x) = 0$ otherwise.  In this talk we will discuss a formula similar to the one of Landau and Gonek that is supported on the product of two prime numbers. We will also look into applications of these formulas.