Alladi Ramakrishnan Hall

Goldback Generating Functions

Gautami Bhowmik

University of Lille 1, France

The central object is the function
$$G(n)=\sum_{n_1+n_2=n}\Lambda(n_1)\Lambda(n_2)$$
where $\Lambda$ is the Von Mangoldt function.
Most of its analytic properties can be studied only assuming
the Riemann Hypothesis. This is what we do for the analytic continuation of the
generating function of $G$ as well as the average orders.