On the zero-free region and the distribution of zeros of the prime zeta function

Abstract

The prime zeta function is one of the most under-researched varieties of the class. Very little is known about the irregular distribution of its zeros. The presented study aims - albeit partially - to fill the gap in our understanding of the subject. We consider the zero-free region of the prime zeta function and verify statistically certain conjectures regarding the distribution patterns of the zeroes of the prime zeta function.

Keywords

• prime zeta function
• zeta function zeros
• zero-free region
• primary 11m41
• secondary 11m99