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- W4285483756 abstract "We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers $p$. We offer an elementary approach based on a counting method. The outcome is a weak form of the Lang-Weil lower bound for the number of solutions modulo $p$, only differing from Lang-Weil by an asymptotic $p^epsilon$ multiplicative factor. Our second contribution is a reduction lemma to the case of a single equation which we use to extend our results to systems of equations. We show further how to use this reduction to prove the full Lang-Weil estimate for varieties, assuming it for hypersurfaces, in a version using a variant of the classical degree in the error term." @default.
- W4285483756 created "2022-07-15" @default.
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- W4285483756 date "2022-10-06" @default.
- W4285483756 modified "2023-10-13" @default.
- W4285483756 title "Polynomial equations modulo prime numbers" @default.
- W4285483756 hasPublicationYear "2022" @default.
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