Distribution of roots of polynomial congruences

Igor E. Shparlinski

doi:10.1155/2007/37853

Distribution of roots of polynomial congruences

Igor E. Shparlinski

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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+ε; for any fixed ε < 0 and sufficiently large p.

Original language	English
Article number	37853
Pages (from-to)	1-5
Number of pages	5
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2007
DOIs	https://doi.org/10.1155/2007/37853
Publication status	Published - 2007

Bibliographical note

Copyright the Author(s) 2007. Version archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further reproduction rights please contact the publisher at http://www.hindawi.com/.

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title = "Distribution of roots of polynomial congruences",

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 ≥ pd/2+ε; for any fixed ε < 0 and sufficiently large p.",

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AB - 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 ≥ pd/2+ε; for any fixed ε < 0 and sufficiently large p.

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

M1 - 37853

ER -

Distribution of roots of polynomial congruences

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