On the solvability of general cubic equations over Z(P)*

• Main Authors: Saburov, Mansoor, Ahmad, Mohd Ali Khameini
• Format: Article
• Language: English; English; English
• Published: Science Society Thailand 2017
• Subjects: Q Science (General)
• Online Access: http://irep.iium.edu.my/58697/1/58697_On%20the%20solvability%20of%20general%20cubic.pdf; http://irep.iium.edu.my/58697/2/58697_On%20the%20solvability%20of%20general%20cubic_WOS.pdf; http://irep.iium.edu.my/58697/13/58697_On%20the%20solvability%20of%20general%20cubic_SCOPUS.pdf; http://irep.iium.edu.my/58697/; http://www.scienceasia.org/2017.43S.n1/scias43S_1.pdf
• Institution: Universiti Islam Antarabangsa Malaysia

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.