Cyclic polynomials in Dirichlet-type spaces of the unit bidisk

For α ∈ R, α ∈ R , we consider the scale of function spaces, namely the Dirichlet-type space Dα D α consisting of holomorphic functions on the unit bidisk D² D 2 , f(z,w)=∑ k,l=0∞aₖₗzᵏwˡ f ( z , w ) = ∑ k , l = 0 ∞ a kl z k w l such that aligned ∑ k,l=0∞(k+l+1)^α |aₖₗ|² < ∞ . aligned ∑ k , l = 0 ∞ ( k + l + 1 ) α | a kl | 2 < ∞ . In this paper, we solve an open problem posed by Torkinejad Ziarati concerning the cyclicity of the polynomial 2-z₁-z₂ 2 - z 1 - z 2 in D_α D α for 3/2 < α ≤ 2 3 2 < α ≤ 2 . We provide an affirmative answer and, as a consequence, complete the characterization of cyclic polynomials in D_α