His most important article is . In this paper, he succeeded in proving a converse to Abel's theorem for the first time: this result was the starting point of numerous investigations, leading to the proof and to applications of several theorems of such kind for various summability methods. The statement of these theorems has a standard structure: if a series is summable according to a given summability method and satisfies an additional condition, called ""Tauberian condition"", then it is a convergent series. Starting from 1913 onward, G. H. Hardy and J. E. Littlewood used the term "Tauberian" to identify this class of theorems. Describing with a little more detail Tauber's 1897 work, it can be said that his main achievements are the following two theorems: