On the solvability of general cubic equations over Z(P)* - Saburov, Mansoor; Ahmad, Mohd Ali Khameini (Science Society Thailand, 2017)
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.