Mathematics of Computation

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

Author(s): Yoshiyuki Kitaoka.
Journal: Math. Comp. 78 (2009), 523-536.
MSC (2000): Primary 11K99, 11C08, 11Y05
Posted: May 12, 2008
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Abstract: Let be a monic polynomial in $\mathbb{Z}[x]$ . We observe a statistical relation of roots of in different local fields $\mathbb{Q}_p$ , where decomposes completely. Based on this, we propose several conjectures.

References:

1.: T. Hadano, Y. Kitaoka, T. Kubota, M. Nozaki, Densities of sets of primes related to decimal expansion of rational numbers, Number Theory: Tradition and Modernization, pp. 67-80, W. Zhang and Y. Tanigawa, eds., Springer, New York, 2006. MR 2213829 (2007b:11110)

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Additional Information:

Yoshiyuki Kitaoka
Affiliation: Department of Mathematics, Meijo University, Tenpaku, Nagoya, 468-8502, Japan
Email: kitaoka@ccmfs.meijo-u.ac.jp

DOI: 10.1090/S0025-5718-08-02133-9
PII: S 0025-5718(08)02133-9
Keywords: Statistics, roots of polynomial, local field
Received by editor(s): May 7, 2007
Received by editor(s) in revised form: December 10, 2007
Posted: May 12, 2008
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C), The Ministry of Education, Science, Sports and Culture.
Copyright of article: Copyright 2008, American Mathematical Society


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