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Scattering for time series with an application to the zeta function of an algebraic curve

Jean-Francois Burnol
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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).

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BibTeXRIS

Jean-Francois Burnol. 1999-11-23. Scattering for time series with an application to the zeta function of an algebraic curve. https://arxiv.org/abs/math/9911175

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