<abstract xmlns="http://www.w3.org/1999/xhtml">

For polynomials <italic>f</italic> (<italic>x</italic>),<italic>g</italic>1(<italic>x</italic>),<italic>g</italic>2(<italic>x</italic>)over ℤ, we report several observations about the density of primes <italic>p</italic> for which <italic>f</italic> (<italic>x</italic>) is fully splitting at <italic>p</italic> and <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_udt-2023-0002_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><mo>{</mo> <mrow><mfrac><mrow><msub><mrow><mi>g</mi></mrow><mn>1</mn></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow><mi>p</mi></mfrac></mrow> <mo>}</mo></mrow><mo>&lt;</mo><mrow><mo>{</mo> <mrow><mfrac><mrow><msub><mrow><mi>g</mi></mrow><mn>2</mn></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mrow><mi>p</mi></mfrac></mrow> <mo>}</mo></mrow></mrow></math>
<tex-math>\left\{ {{{{g_1}\left( r \right)} \over p}} \right\} &lt; \left\{ {{{{g_2}\left( r \right)} \over p}} \right\}</tex-math>
</alternatives>
</inline-formula> for some root <italic>r</italic> of <italic>f</italic> (<italic>x</italic>) ≡ 0 mod <italic>p</italic>.
</abstract>

For polynomials f (x),g1(x),g2(x)over ℤ, we report several observations about the density of primes p for which f (x) is fully splitting at p and 


{ g1(r)p }<{ g2(r)p }
\left\{ {{{{g_1}\left( r \right)} \over p}} \right\} < \left\{ {{{{g_2}\left( r \right)} \over p}} \right\}

 for some root r of f (x) ≡ 0 mod p.

Notes on the Distribution of Roots Modulo Primes of a Polynomial IV

Uniform distribution theory

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

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

For polynomials f (x),g1(x),g2(x)over ℤ, we report several observations about the density of primes p for which f (x) is fully splitting at p and 


{ g1(r)p...

Notes on the Distribution of Roots Modulo Primes of a Polynomial IV

Pubblicato online: 10 ago 2023

Pagine: 9 - 30

Ricevuto: 16 ago 2022

Accettato: 12 dic 2022

DOI: https://doi.org/10.2478/udt-2023-0002

Parole chiave
equidistribution, polynomial, roots modulo a prime

© 2023 Yoshiyuki Kitaoka, published by Sciendo

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

Notes on the Distribution of Roots Modulo Primes of a Polynomial IV

Pubblicato online: 10 ago 2023

Pagine: 9 - 30

Ricevuto: 16 ago 2022

Accettato: 12 dic 2022

DOI: https://doi.org/10.2478/udt-2023-0002

Parole chiaveequidistribution, polynomial, roots modulo a prime

© 2023 Yoshiyuki Kitaoka, published by Sciendo

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

Parole chiave
equidistribution, polynomial, roots modulo a prime