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- Title
On the solvability of general cubic equations over Z<sub>p</sub>.
- Authors
Saburov, Mansoor; Ahmad, Mohd Ali Khameini
- Abstract
The p-adic models of statistical mechanics require an investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is whether a root of a polynomial equation belongs to some given domains. In this paper, we study the solvability of general cubic equations over Z*p where prime p > 3. Our investigation enables us to describe all translation invariant p-adic Gibbs measures on a Cayley tree of order three.
- Subjects
P-adic fields; CUBIC equations; STATISTICAL mechanics; HILBERT'S tenth problem; ANALYTIC functions
- Publication
ScienceAsia, 2017, Vol 43, p1
- ISSN
1513-1874
- Publication type
Article
- DOI
10.2306/scienceasia1513-1874.2017.43S.001