The problem of when a given sequence (resp. two sequences) of complex points can be the zero-sequence(s) of a solution (resp. of two linearly independent solutions) of f '' + A ( z ) f = 0, where A ( z ) is entire, has been studied by several authors during the last two decades. However, it is not well-known that problems of this type were first stated and studied by O. Boruvka and V. Seda almost fifty years ago. A historical review to these studies will be given below. We then offer some remarks and improvements on results due to S. Bank and A. Sauer found. Our reasoning towards these improvements is based on some growth estimates for Mittag-Leffler-type series in the complex plane. These estimates might be of independent interest.