#### 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.

Done