On explicit upper and lower bounds for the Selberg class functions

2:00 pm, Wednesday, 6th November

Abstract

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 upper bounds for logarithms and logarithmic derivatives of the Selberg class functions when ℜ(𝑠)>1/2. In the case of logarithms, I will discuss also about lower bounds for the Selberg class functions.

All results are under the Generalized Riemann hypothesis. In some of the results, we additionally assume some additional hypothesis including a polynomial Euler product representation, the strong 𝜆-conjecture or assumptions related to the Selberg’s (normality) conjecture. The talk is based on a joint work with Aleksander Simonic (University of New South Wales Canberra).