1999/10/22 by Masato Kuwata, Kuwata, Masato, Jaap Top +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.math/9910191
arxiv created 1999/10/22 · openalex publication_date 1999/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We study the surface arising from the diophantine equation m3+(m+1)3+...+(m+k-1)3=l2. It turns out that this is a K3 surface with Picard number 20. We stduy its aritmetic properties in detail. We construct elliptic fibrations on it, and we find a parametric solution to the original equation. Also, we determine the Hasse-Weil zeta function of the surface over Q.