A characterization of a generalized order of analytic functions of several complex variables by means of polynomial approximation and interpolation is established.

We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.

Let K be a compact set in ℂ, f a function analytic in ℂ̅∖K vanishing at ∞. Let $f\left(z\right)={\sum }_{k=0}^{\infty }{a}_k{z}^{-k-1}$ be its Taylor expansion at ∞, and $H_s\left(f\right)=det{\left(a_{k+l}\right)}_{k,l=0}^s$ the sequence of Hankel determinants. The classical Pólya inequality says that $limsu{p}_{s\to \infty }{\left|H_s\left(f\right)\right|}^{1/s²}\le d\left(K\right)$, where d(K) is the transfinite diameter of K. Goluzin has shown that for some class of compacta this inequality is sharp. We provide here a sharpness result for the multivariate analog of Pólya’s inequality, considered by the second author in Math. USSR Sbornik 25 (1975), 350-364.

By considering a question proposed by F. Gross concerning unique range sets of entire functions in $ℂ$, we study the unicity of meromorphic functions in ${ℂ}^m$ that share three distinct finite sets CM and obtain some results which reduce $5\le c_3\left(ℳ\left({ℂ}^m\right)\right)\le 9$ to $5\le c_3\left(ℳ\left({ℂ}^m\right)\right)\le 6$.