Mahler's measures on function spaces (Q351835)

In this paper the author defines some analogues of Mahler measure in function spaces following the work of Pritsker who considered a Bergman-space version of Mahler's measure. Among the many results of this paper, the author proves that if \(f\) is a \textit{Nevanlinna function} over the unit disc, i.e. an analytic function whose subharmonic function \(\log^{+} |f|\) has a harmonic majorant, and \(P_n\) is a sequence of integer polynomials satisfying \(\lim_{n \to \infty} M(f-P_n)=0\) then \(f\) must be an integer polynomial. He also gives an equivalent version of Lehmer's conjecture in terms of a Fock-space analogue of Mahler's measure which is introduced in this paper.