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On the Chevalley-Warning Theorem When the Degree Equals the Number of Variables

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Abstract

Let f be a degree d polynomial in n variables defined over a finite field k of characteristic p and let N be the number of zeros of f in kn. The Chevalley-Warning theorem asserts that if d<n, then N is divisible by p. In this note we show a version of the result for d = n.

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Acknowledgements

This research was supported by ANID (ex CONICYT) FONDECYT Regular grant 1190442 from Chile.

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  1. Departamento de Matemáticas, Pontificia Universidad Católica de Chile Facultad de Matemáticas, 4860 Av. Vicuña Mackenna, Macul, RM, Chile

    Hector Pasten

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  1. Hector Pasten
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Correspondence to Hector Pasten.

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Pasten, H. On the Chevalley-Warning Theorem When the Degree Equals the Number of Variables. Combinatorica 42 (Suppl 2), 1481–1486 (2022). https://doi.org/10.1007/s00493-022-5043-x

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  • DOI: https://doi.org/10.1007/s00493-022-5043-x

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