On cubic equations over p-adic fields

DOI10.1142/S1793042114500201zbMath1307.11124arXiv1204.1743MaRDI QIDQ2876598

Mansoor Saburov, Bakhrom A. Omirov, Farrukh Mukhamedov

Publication date: 19 August 2014

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.1743

zbMATH Keywords

numbers of solutions\(p\)-adic fieldssolvability criteriacubic equations\(p\)-adic Cardano formula

Mathematics Subject Classification ID

Cubic and quartic Diophantine equations (11D25) Special polynomials in general fields (12E10) Polynomials (11S05) (p)-adic and power series fields (11D88)

Related Items (17)

Chaos in p-adic Statistical Lattice Models: Potts Model ⋮ Chaotic behavior of the p-adic Potts–Bethe mapping II ⋮ Solvability of cubic equations in \(p\)-adic integers \((p>3)\) ⋮ The \(p\)-adic Ising model in an external field on a Cayley tree: periodic Gibbs measures ⋮ The description of generalized translation-invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three ⋮ Periodic points of a \(p\)-adic operator and their \(p\)-adic Gibbs measures ⋮ p$$ p $$‐Adic phase transitions for countable state Potts model ⋮ Trinomial equations of degree 6 over \(\mathbb{Q}_p \) ⋮ \(p\)-adic dynamical systems of \((3,1)\)-rational functions with unique fixed point ⋮ Phase transition for thep-adic Ising–Vannimenus model on the Cayley tree ⋮ Local descriptions of roots of cubic equations over \(p\)-adic fields ⋮ Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures ⋮ Renormalization method in \(p\)-adic \(\lambda\)-model on the Cayley tree ⋮ On \(G_2\)-periodic quasi Gibbs measures of \(p\)-adic Potts model on a Cayley tree ⋮ On periodic \(p\)-adic generalized Gibbs measures for Ising model on a Cayley tree ⋮ On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions ⋮ On descriptions of all translation invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three

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