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Mathematics of Computation

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

Author: Yoshiyuki Kitaoka
Journal: Math. Comp. 78 (2009), 523-536
MSC (2000): Primary 11K99, 11C08, 11Y05
Published electronically: May 12, 2008
MathSciNet review: 2448719
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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.

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Additional Information

Yoshiyuki Kitaoka
Affiliation: Department of Mathematics, Meijo University, Tenpaku, Nagoya, 468-8502, Japan

Keywords: Statistics, roots of polynomial, local field
Received by editor(s): May 7, 2007
Received by editor(s) in revised form: December 10, 2007
Published electronically: 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.
Article copyright: © Copyright 2008 American Mathematical Society

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