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Uniform Distribution Theory
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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 15. Issue 1


Published on

June, 2020


Pages

93-104


DOI

https://doi.org/10.2478/udt-2020-0005

Article

Notes on the Distribution of Roots Modulo a Prime of a Polynomial III


Authors

Yoshiyuki Kitaoka


Abstract

Let f (x) bea monicpolynomialwith integer coefficients and integers r1,..., rn with 0 ≤ r1 ≤··· ≤ rn <p the n roots of f (x) ≡ 0mod p for a prime p. We proposed conjectures on the distribution of the point (r1/p,...,rn/p) in the previous papers. One aim of this paper is to revise them for a reducible polynomial f (x), and the other is to show that they imply the one-dimensional equidistribution of r1/p,...,rn/p for an irreducible polynomial f (x) by a geometric way.


Citation

Kitaoka, Y. (2020). Notes on the Distribution of Roots Modulo a Prime of a Polynomial III. Uniform distribution theory, 15(1), 93-104. https://doi.org/10.2478/udt-2020-0005