English

Regular Polygonal Vortex Filament Evolution and Exponential Sums

Number Theory 2024-07-16 v2

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 MM sides under the vortex filament equation. The proof depends on showing that some exponential sums with arithmetic content are purely imaginary.

Cite

@article{arxiv.2403.17758,
  title  = {Regular Polygonal Vortex Filament Evolution and Exponential Sums},
  author = {Fernando Chamizo and Francisco de la Hoz},
  journal= {arXiv preprint arXiv:2403.17758},
  year   = {2024}
}

Comments

9 pages, 1 figure

R2 v1 2026-06-28T15:34:15.814Z