Article
On the Distribution of Polynomials With Bounded Roots Ii. Polynomials With Integer Coefficients
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Abstract
In the present paper we give a new type of statistical results on the distribution of integral polynomials of given degree. The main feature of our formula is that we can see a clear distinction with respect to the signature of poly- nomials. For example, we see that among certain polynomials in question, totally real ones are very rare. Further we show that reducible polynomials are negligible in every formula. We derive asymptotic results on Pisot, Salem and expanding polynomials that often appear as dilation constants of dynamical systems.
Keywords
Distribution of integer polynomials, Pisot numbers, Salem numbers, expanding.
Citation
Akiyama, S. & Petho, A. (2014). On the distribution of polynomials with bounded roots ii. polynomials with integer coefficients. Uniform Distribution Theory, 9(1), 5–19.
S. Akiyama and A. Petho, “On the distribution of polynomials with bounded roots ii. polynomials with integer coefficients,” Uniform Distribution Theory, vol. 9, no. 1, pp. 5–19, 2014.
Akiyama S, Petho A. On the distribution of polynomials with bounded roots ii. polynomials with integer coefficients. Uniform Distribution Theory. 2014;9(1):5–19.
Akiyama, S. and Petho, A. (2014), ‘On the distribution of polynomials with bounded roots ii. polynomials with integer coefficients’, Uniform Distribution Theory, 9(1), pp. 5–19.
Akiyama, Shigeki, and Attila Petho. “On the Distribution of Polynomials with Bounded Roots Ii. Polynomials with Integer Coefficients.” Uniform Distribution Theory, vol. 9, no. 1, 2014, pp. 5–19.
Akiyama, Shigeki, and Attila Petho. “On the Distribution of Polynomials with Bounded Roots Ii. Polynomials with Integer Coefficients.” Uniform Distribution Theory 9, no. 1 (2014): 5–19.
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Published by: Engineering Journals
