Full metadata

Title
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
2014-11-01
Contributors
Resource Type
Text
Extent
24 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
ASU Scholarship Showcase
Identifier
Digital object identifier: 10.1142/S179304211450050X
International standard serial number
1793-0421
International standard serial number
1793-7310
Peer-reviewed
No
Open Access
No
Series
INTERNATIONAL JOURNAL OF NUMBER THEORY
Handle
https://hdl.handle.net/2286/R.I.27267
Preferred Citation

Bremner, Andrew, Choudhry, Ajai, & Ulas, Maciej (2014). Constructions of diagonal quartic and sextic surfaces with infinitely many rational points. INTERNATIONAL JOURNAL OF NUMBER THEORY, 10(7), 1675-1698. http://dx.doi.org/10.1142/S179304211450050X

Level of coding
minimal
Cataloging Standards
asu1
Note
Electronic version of an article published in INTERNATIONAL JOURNAL OF NUMBER THEORY, 10, 7, 2014, 1675-1698 Copyright World Scientific Publishing Company http://dx.doi.org/10.1142/S179304211450050X
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  • 2015-01-16 11:39:52
System Modified
  • 2021-10-26 04:31:09
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