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On cubic polynomials III. Systems ofp-adic equations

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Abstract

We study systems of equations

$$\mathfrak{F}_1 = \ldots = \mathfrak{F}_r = 0,$$

where\(\mathfrak{F}_1 , \ldots ,\mathfrak{F}_r \) are cubic forms withp-adic coefficients. Such a system has a nontrivialp-adic solution if the number of variables is at least 50,000 ·r 3. Further we will give estimates for the number of solutions of certain systems of cubic congruences.

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Authors and Affiliations

  1. Mathematics Department, University of Colorado, 80309, Boulder, CO, U.S.A.

    Wolfgang M. Schmidt

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  1. Wolfgang M. Schmidt
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Partially supported by NSF contract NSF-MCS-8015356.

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Schmidt, W.M. On cubic polynomials III. Systems ofp-adic equations. Monatshefte für Mathematik 93, 211–223 (1982). https://doi.org/10.1007/BF01299298

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  • DOI: https://doi.org/10.1007/BF01299298

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