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

Yoshiyuki Kitaoka

doi:10.1515/udt-2017-0017

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

Uniform distribution theory

Volume 12 (2017): Issue 2 (December 2017)

By: Yoshiyuki Kitaoka

Open Access

|Jan 2018

Abstract

Let f(x) be a monic polynomial in Z[x] with roots α₁, . . ., α_n. We point out the importance of linear relations among 1, α₁, . . . , α_n over rationals with respect to the distribution of local roots of f modulo a prime. We formulate it as a conjectural uniform distribution in some sense, which elucidates data in previous papers.

References

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2017-0017 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 91 - 117

Submitted on: Oct 5, 2016

Accepted on: Jan 19, 2017

Published on: Jan 30, 2018

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

11K

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2018 Yoshiyuki Kitaoka, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 12 (2017): Issue 2 (December 2017)