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arXiv · 2403.17758

Regular Polygonal Vortex Filament Evolution and Exponential Sums

Fernando Chamizo·Francisco de la Hoz
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Abstract

In this paper, we give a rigorous proof for the expression of the angle between adjacent sides in the skew polygons appearing at rational times in the evolution of regular polygons of $M$ sides under the vortex filament equation. The proof depends on showing that some exponential sums with arithmetic content are purely imaginary.

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Fernando Chamizo, Francisco de la Hoz. 2024-03-26. Regular Polygonal Vortex Filament Evolution and Exponential Sums. https://arxiv.org/abs/2403.17758

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