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In this paper, we construct several infinite families of diagonal quartic surfaces ax[superscript 4] + by[superscript 4] + cz[superscript 4] + dw[superscript 4] = 0 (where a, b, c, d

In this paper, we construct several infinite families of diagonal quartic surfaces ax[superscript 4] + by[superscript 4] + cz[superscript 4] + dw[superscript 4] = 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.

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Date Created
  • 2014-11-01
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  • Text
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    Identifier
    • Digital object identifier: 10.1142/S179304211450050X
    • Identifier Type
      International standard serial number
      Identifier Value
      1793-0421
    • Identifier Type
      International standard serial number
      Identifier Value
      1793-7310
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    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

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