Distribution of Roots of Polynomial Congruences

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2007 English Publisher:Hindawi LimitedJournal:International Journal of Mathematics and Mathematical Sciences, volume 2,007, pages 1-5 (issn: 0161-1712, eissn: 1687-0425,

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Authors: Igor E. Shparlinski;

doi: 10.1155/2007/37853

Distribution of Roots of Polynomial Congruences

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Abstract

For a primep, we obtain an upper bound on the discrepancy of fractionsr/p, whererruns through all of roots modulopof all monic univariate polynomials of degreedwhose vector of coefficients belongs to ad-dimensional boxℬ. The bound is nontrivial starting with boxesℬof size|ℬ|≥pd/2+ɛfor any fixedɛ<0and sufficiently largep.

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Macquarie University
Australia

Keywords

Irregularities of distribution, discrepancy, QA1-939, discrepancy, Distribution modulo one, Polynomial congruences, Mathematics

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