A statistical relation of roots of a polynomial in different local fields

Kitaoka, Yoshiyuki

doi:10.1090/S0025-5718-08-02133-9

A statistical relation of roots of a polynomial in different local fields
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by Yoshiyuki Kitaoka;

Math. Comp. 78 (2009), 523-536

DOI: https://doi.org/10.1090/S0025-5718-08-02133-9

Published electronically: May 12, 2008

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Abstract:

Let $f(x)$ be a monic polynomial in $\mathbb {Z}[x]$. We observe a statistical relation of roots of $f(x)$ in different local fields $\mathbb {Q}_p$, where $f(x)$ decomposes completely. Based on this, we propose several conjectures.

References

Toshihiro Hadano, Yoshiyuki Kitaoka, Tomio Kubota, and Michihiro Nozaki, Densities of sets of primes related to decimal expansion of rational numbers, Number theory, Dev. Math., vol. 15, Springer, New York, 2006, pp. 67–80. MR 2213829, DOI 10.1007/0-387-30829-6_{6}