On an extension of the Landau-Gonek formula

Farzad Aryan, McGill University

Let $\rho$ be zero of the Riemann zeta function. The Landau-Gonek formula asserts that
$$
\sum_{0 $$
where $\lambda(n) = \log p$ if $n = p^i$ and $\lambda(n) = 0$ otherwise. Roughly speaking, the formula says that the support of the above sum is on prime numbers. In this talk we will discuss a formula similar to (I) that is supported on the product of two prime numbers. We will also look into applications of these formulas.

MC 5501