arXiv subjects
Publications and source records attributed to Adan Medrano Martin del Campo.
We provide an elementary approach to computing the quadratic Gauss sum, emphasizing the method employed to compute the sum corresponding to multiples of 4. The proof method employed does not rely on the law of quadratic reciprocity, but only on exploiting symmetries among the sum's components, together with a recursive approach.
Every graph $Γ$ can be embedded in the plane with a minimal number of edge intersections, called its classical crossing number $\text{cross}\left(Γ\right)$. In this paper, we prove that if $Γ$ is a metric graph it can be realized as a tropical curve in the plane with exactly $\text{cross}\left(Γ\right)$ crossings, where the tropical curve is equipped with the lattice length metric. Our result has an application in algebraic geometry, as it enables us to construct a rational map of non-Archimedean curves into the projective plane, whose tropicalization is almost faithful when restricted to their skeleton.