Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...

Dynamical systems theory provides a rigorous framework to analyse how points evolve with time according to deterministic rules. At its heart lies the study of chaotic behaviour, hyperbolicity and the ...

This article considers linear relations between the nontrivial zeroes of the Riemann zeta-function. The main application is an alternative disproof of Mertens' conjecture by showing that lim supx→∞ ...

It is known that the Lerch (or periodic) zeta function of nonpositive integer order, l _n (ξ), n Є No := {0,1,2,3,...}, is a polynomial in cot(πξ) of degree n+1. In this paper, a very simple explicit ...