Universal series and fundamental solutions of the Cauchy-Riemann operator (Q2378563)

Recently \textit{P. M. Gauthier} and \textit{N. Tarkhanov} [Complex Variables, Theory Appl. 50, No. 3, 211--215 (2005; Zbl 1101.30038)] obtained the following result: If \(K\) is any compact subset of \(\mathbb{C}\) and if \(K\) is a function holomorphic on some neighborhood of \(K\), then \(f\) can be approximated, uniformly on \(K\), by linear combinations of shifts of the Riemann zeta function \(\zeta\). In the present paper the author shows that if the complement of the compact set is connected, then the function \(f\) can be uniformly approximated on \(K\) by a finite linear combination of shifts of \(\zeta\) by points belonging to a prescribed countable set.