On the system of the functions zeta(s)/(s-rho)^k

TL;DR

This paper investigates the completeness, minimality, and hereditary completeness of a system of functions derived from the zeta function within a specific sub-Hilbert space on the critical line.

Contribution

It extends the understanding of the system's properties by examining hereditary completeness, a question not addressed in prior work.

Findings

The system is complete and minimal in the considered sub-Hilbert space.

Hereditary completeness of the system remains an open question.

Provides insights into the structure of zeta-related function systems.

Abstract

The system of the functions zeta(s)/(s-rho)^k is complete and minimal in a certain sub-Hilbert space of the L^2 space of the critical line. We study whether it is also hereditarily complete.