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Volume 43S Number 1 Volume 43 Number 1

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Research articles

ScienceAsia 43S(2017): 1-8 |doi: 10.2306/scienceasia1513-1874.2017.43S.001


On the solvability of general cubic equations over ℤp*


Mansoor˙Saburov*, Mohd˙Ali˙Khameini˙Ahmad

 
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 ℤp* where prime p>3. Our investigation enables us to describe all translation invariant p-adic Gibbs measures on a Cayley tree of order three.

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Faculty˙of˙Science, International˙Islamic˙University˙Malaysia, 25200˙Kuantan, Pahang, Malaysia

* Corresponding author, E-mail: msaburov@gmail.com

Received 22 Aug 2014, Accepted 21 May 2017