Article
Notes on the Distribution of Roots Modulo a Prime of a Polynomial Iii
Authors
Abstract
Let f (x) be a monic polynomial with integer coefficients and in- tegers r 1 , . . . , r n with 0 ≤ r 1 ≤ · · · ≤ r n < p the n roots of f (x) ≡ 0 mod p for a prime p. We proposed conjectures on the distribution of the point (r 1 /p, . . . , r n /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 r 1 /p, . . . , r n /p for an irreducible polynomial f (x) by a geo- metric way.
Keywords
Equidistribution, polynomial, roots modulo a prime.
Citation
(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
Y. K., “Notes on the distribution of roots modulo a prime of a polynomial iii,” Uniform Distribution Theory, vol. 15, no. 1, pp. 93–104, 2020, doi: 10.2478/udt-2020-0005.
YK. Notes on the distribution of roots modulo a prime of a polynomial iii. Uniform Distribution Theory. 2020;15(1):93–104. doi:10.2478/udt-2020-0005.
(2020), ‘Notes on the distribution of roots modulo a prime of a polynomial iii’, Uniform Distribution Theory, 15(1), pp. 93–104. Available at: https://doi.org/10.2478/udt-2020-0005.
, Yoshiyuki Kitaoka. “Notes on the Distribution of Roots Modulo a Prime of a Polynomial Iii.” Uniform Distribution Theory, vol. 15, no. 1, 2020, pp. 93–104. https://doi.org/10.2478/udt-2020-0005.
, Yoshiyuki Kitaoka. “Notes on the Distribution of Roots Modulo a Prime of a Polynomial Iii.” Uniform Distribution Theory 15, no. 1 (2020): 93–104. https://doi.org/10.2478/udt-2020-0005.
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Published by: Engineering Journals
