Conditional estimates for logarithms and logarithmic derivatives in the Selberg class — Neea Palojarvi (Université d'Helsinki)Séminaire « Arithmétique »
The Selberg class consists of functions sharing similar properties to the Riemann zeta function. The Riemann zeta function is one example of the functions in this class. The estimates for logarithms of Selberg class functions and their logarithmic derivatives are connected to, for example, primes in arithmetic progressions.
In this talk, I will discuss about effective and explicit estimates for logarithms and logarithmic derivatives of the Selberg class functions when $\Re(s) \geq 1/2+\delta$ where $\delta>0$. All results are under the Generalized Riemann hypothesis and some of them are also under assumption of a polynomial Euler product representation or the strong $\lambda$-conjecture. The talk is based on a joint work with Aleksander Simonič (University of New South Wales Canberra).