On cubic polynomials III. Systems ofp-adic equations |
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Authors: | Prof Dr Wolfgang M Schmidt |
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Institution: | 1. Mathematics Department, University of Colorado, 80309, Boulder, CO, U.S.A.
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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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