Constructions of Diagonal Quartic and Sextic Surfaces With Infinitely Many Rational Points
Description
In this paper, we construct several infinite families of diagonal quartic surfaces ax4 + by4 + cz4 + dw4 = 0 (where a, b, c, d are non-zero integers) with infinitely many rational points and satisfying the condition abcd is not a square. In particular, we present an infinite family of diagonal quartic surfaces defined over ℚ with Picard number equal to one and possessing infinitely many rational points. Further, we present some sextic surfaces of type ax6 + by6 + cz6 + dwi = 0, i = 2, 3, or 6, with infinitely many rational points.
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2014-11-01
Agent
- Author (aut): Bremner, Andrew
- Author (aut): Choudhry, Ajai
- Author (aut): Ulas, Maciej
- Contributor (ctb): College of Liberal Arts and Sciences