On the number of zeros of diagonal cubic forms

Gerald Myerson

doi:10.1016/0022-314X(79)90023-4

On the number of zeros of diagonal cubic forms

Gerald Myerson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

We extend to finite fields in general the results proved, in a recent paper (J. Number Theory 9 (1977)) with the same title as the current work, by Chowla, Cowles, and Cowles for the prime fields. The results concern the dependence on s of the number of solutions of the equation x₁ ³ + x₂ ³ + ⋯ + x₃ ³ = 0. We also give results for the equation x₁ ⁴ + x₂ ⁴ + ⋯ + x₈ ⁴ = 0.

Original language	English
Pages (from-to)	95-99
Number of pages	5
Journal	Journal of Number Theory
Volume	11
Issue number	1
DOIs	https://doi.org/10.1016/0022-314X(79)90023-4
Publication status	Published - 1979
Externally published	Yes

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10.1016/0022-314X(79)90023-4

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title = "On the number of zeros of diagonal cubic forms",

abstract = "We extend to finite fields in general the results proved, in a recent paper (J. Number Theory 9 (1977)) with the same title as the current work, by Chowla, Cowles, and Cowles for the prime fields. The results concern the dependence on s of the number of solutions of the equation x1 3 + x2 3 + ⋯ + x3 3 = 0. We also give results for the equation x1 4 + x2 4 + ⋯ + x8 4 = 0.",

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AB - We extend to finite fields in general the results proved, in a recent paper (J. Number Theory 9 (1977)) with the same title as the current work, by Chowla, Cowles, and Cowles for the prime fields. The results concern the dependence on s of the number of solutions of the equation x1 3 + x2 3 + ⋯ + x3 3 = 0. We also give results for the equation x1 4 + x2 4 + ⋯ + x8 4 = 0.

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On the number of zeros of diagonal cubic forms

Abstract

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