Some conditional estimates for functions in the Selberg class

10:00 am, Monday, 27th November

Abstract

In this talk I will present recent progress in obtaining conditional (GRH) estimates for $(\mathcal{L}'/\mathcal{L})(s)$ and $\log{\mathcal{L}(s)}$, when $\mathcal{L}$ is an element in the Selberg class of functions. The results are divided into two groups, according to whether $s$ is close to the critical line or not. We are able to obtain effective results while assuming the strong $\lambda$-conjecture and a polynomial Euler product representation for $\mathcal{L}$. This is a joint work with N. Paloj\"{a}rvi (The University of Helsinki).