<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>f</italic> (<italic>x</italic>) be a monic polynomial with integer coefficients and 0 ≤ <italic>r</italic>1 ≤ ··· ≤ <italic>r</italic>n<italic>&lt;p</italic> its roots modulo a prime <italic>p</italic>. We generalize a conjecture on the distribution of roots <italic>r</italic><italic>i</italic> with additional congruence relations <italic>r</italic><italic>i</italic> ≡ <italic>R</italic><italic>i</italic> mod <italic>L</italic> from the case that <italic>f</italic> has no non-trivial linear relation among roots to the case that <italic>f</italic> has a non-trivial linear relation.</abstract>

Let f (x) be a monic polynomial with integer coefficients and 0 ≤ r1 ≤ ··· ≤ rn<p its roots modulo a prime p. We generalize a conjecture on the distribution of roots ri with additional congruence relations ri ≡ Ri mod L from the case that f has no non-trivial linear relation among roots to the case that f has a non-trivial linear relation.

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

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Notes on the Distribution of Roots Modulo a Prime of a Polynomial II"}

Let f (x) be a monic polynomial with integer coefficients and 0 ≤ r1 ≤ ··· ≤ rn<p its roots modulo a prime p. We generalize a conjecture on the distribution of...

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

Pubblicato online: 27 mar 2020

Pagine: 87 - 104

Ricevuto: 16 mar 2018

Accettato: 28 ago 2018

DOI: https://doi.org/10.2478/udt-2019-0006

Parole chiave
distribution, polynomial, roots modulo a prime

© 2019 Yoshiyuki Kitaoka, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Pubblicato online: 27 mar 2020

Pagine: 87 - 104

Ricevuto: 16 mar 2018

Accettato: 28 ago 2018

DOI: https://doi.org/10.2478/udt-2019-0006

Parole chiavedistribution, polynomial, roots modulo a prime

© 2019 Yoshiyuki Kitaoka, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Parole chiave
distribution, polynomial, roots modulo a prime