Scattering for time series with an application to the zeta function of an algebraic curve
Number Theory
2007-05-23 v1
Abstract
I explain how the Lax-Phillips theory can be applied to a purely innovating time series and compute the corresponding scattering function. I then associate such a time series to an algebraic curve (of genus at least 1) over a finite field and show that the Riemann Hypothesis (proven long ago) holds if and only if the scattering is causal (this causality is not independently established, though).
Keywords
Cite
@article{arxiv.math/9911175,
title = {Scattering for time series with an application to the zeta function of an algebraic curve},
author = {Jean-Francois Burnol},
journal= {arXiv preprint arXiv:math/9911175},
year = {2007}
}
Comments
10 pages, latex with amsfonts