<abstract xmlns="http://www.w3.org/1999/xhtml"> Let f(x) be a monic polynomial in Z[x] with roots α1, . . ., αn. We point out the importance of linear relations among 1, α1, . . . , αn 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.</abstract>

Let f(x) be a monic polynomial in Z[x] with roots α1, . . ., αn. We point out the importance of linear relations among 1, α1, . . . , αn 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.

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

Uniform distribution theory

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

Let f(x) be a monic polynomial in Z[x] with roots α1, . . ., αn. We point out the importance of linear relations among 1, α1, . . . , αn over rationals with...

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

Published Online: Jan 30, 2018

Page range: 91 - 117

Received: Oct 05, 2016

Accepted: Jan 19, 2017

DOI: https://doi.org/10.1515/udt-2017-0017

Keywords
distribution, polynomial, roots modulo a prime

© 2018

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

Published Online: Jan 30, 2018

Page range: 91 - 117

Received: Oct 05, 2016

Accepted: Jan 19, 2017

DOI: https://doi.org/10.1515/udt-2017-0017

Keywordsdistribution, polynomial, roots modulo a prime

© 2018

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

Keywords
distribution, polynomial, roots modulo a prime