Notes on the Distribution of Roots Modulo a Prime of a Polynomial-Reference-Cited by-同舟云学术

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

Published:2017-12-20 Issue:2 Volume:12 Page:91-117
ISSN:2309-5377
Container-title:Uniform distribution theory
language:en
Short-container-title:

Author:

Kitaoka Yoshiyuki¹

Affiliation:

1. Uzunawa 1085-10, Asahi-cho , Mie, 510-8104 JAPAN

Abstract

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.

Publisher

Walter de Gruyter GmbH

Reference9 articles.

1. [1] DUKE, W.-FRIEDLANDER, J.B.-IWANIEC, H.: Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math. (2) 141 (1995), no. 2, 423-441.

2. [2] HADANO, T.-KITAOKA, Y.-KUBOTA, T.-NOZAKI, M.: Densities of sets of primes related to decimal expansion of rational numbers. (W. Zhang and Y. Tanigawa, eds.) In: Number Theory: Tradition and Modernization, The 3rd China-Japan seminar on number theory, Xi’an, China, February 12-16, 2004. Developments. Math. Vol. 15, 2006, Springer, New York, pp. 67-80,

3. [3] KITAOKA, Y.: A statistical relation of roots of a polynomial in different local fields, Math. Comput. 78 (2009), no. 265, 523-536.

4. [4] A statistical relation of roots of a polynomial in different local fields II, (Aoki, Takashi ed. et al.) In: Number Theory: Dreaming in Dreams, Proceedings of The 5th China-Japan seminar, Higashi-Osaka, Japan, August 27-31, 2008. Ser. Number Theory Appl. Vol. 6, 2010, World Sci. Publ., Hackensack, NJ, pp. 106-126.

5. [5] A statistical relation of roots of a polynomial in different local fields III, Osaka J. Math. 49 (2012), 393-420.

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Gibbs manifolds;Information Geometry;2023-07-03

2. Notes on the Distribution of Roots Modulo Primes of a Polynomial IV;Uniform distribution theory;2023-07-01

3. Notes on the Distribution of Roots Modulo a Prime of a Polynomial III;Uniform distribution theory;2020-06-01

4. Notes on the Distribution of Roots Modulo a Prime of a Polynomial II;Uniform distribution theory;2019-06-01