Periodic Jacobi-Perron Algorithms in Cubic Fields and Fundamental Units

Resumo

In this paper, we study the Jacobi-Perron algorithm of (α, α²) and (1/α, 1/α²) where α is the unique real root of monic cubic irreducible polynomials in certain infinite families. We also investigate the associated Hasse-Bernstein units, along with when they are fundamental units in ℤ[α] and ℚ(α).