Resonant Interactions Along the Critical Line of the Riemann Zeta Function

Ronald Fisch

Resonant Interactions Along the Critical Line of the Riemann Zeta Function

Number Theory 2013-11-12 v2

Authors: Ronald Fisch

Abstract

We have studied some properties of the special Gram points of the Riemann zeta function which lie on contour lines ${\bf Im}(\zeta ( s )) = 0$ which do not contain zeroes of $\zeta ( s )$ . We find that certain functions of these points, which all lie on the critical line ${\bf Re}( s ) = 1/2$ , are correlated in remarkable and unexpected ways. We have data up to a height of $t = 10^4$ , where $s = \sigma + it$ .

Keywords

Riemann zeta function Gram points critical line resonant interactions contour lines zero-free regions

Cite

@article{arxiv.1309.4793,
  title  = {Resonant Interactions Along the Critical Line of the Riemann Zeta Function},
  author = {Ronald Fisch},
  journal= {arXiv preprint arXiv:1309.4793},
  year   = {2013}
}

Comments

15 pages, 16 figures; more data, minor corrections and improvements. arXiv admin note: substantial text overlap with arXiv:1210.3618

Resonant Interactions Along the Critical Line of the Riemann Zeta Function

Abstract

Keywords

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