On the Riemann zeta-function, Parts IV-V
Abstract
In Part I an odd meromorphic function f(s) has been constructed from the Riemann zeta-function evaluated at one-half plus s. The conjunction of the Riemann hypothesis and hypotheses advanced by the author in Part I is assumed. In Part IV we derive the two-sided Laplace transform representation of f(s) on the open vertical strip V of all s with real part between zero and four. An additional hypothesis is used to prove that the Laplace density of f(s) on the strip V is positive. Let z(n) be the nth critical zero of the Riemann zeta-function of positive imaginary part in order of magnitude thereof. In Part V an expression is derived for z(1). A relation is obtained of the pair z(n) and the first derivative thereat of the zeta-function to the preceding such pairs.
Cite
@article{arxiv.0705.4593,
title = {On the Riemann zeta-function, Parts IV-V},
author = {Anthony Csizmazia},
journal= {arXiv preprint arXiv:0705.4593},
year = {2007}
}