Distribution of Roots of Polynomial Congruences

Igor E. Shparlinski

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-5

Abstract:

For a prime p , we obtain an upper bound on the discrepancy of fractions r / p , where r runs through all of roots modulo p of all monic univariate polynomials of degree d whose vector of coefficients belongs to a d -dimensional box ℬ . The bound is nontrivial starting with boxes ℬ of size | ℬ | ≥ p d / 2 + ɛ for any fixed ɛ < 0 and sufficiently large p .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:037853

DOI: 10.1155/2007/37853

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