Seminar

Speaker(s): 
Farzad Aryan, University of Montreal
Title: 
On an extension of the Landau-Gonek formula
Abstract: 

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.