An extension of a theorem of Eisenstein

Abstract

In the present paper I obtain an extension of the so-called Eisenstein theorem which is proved by means of Riemann-Stieltjes integration.

Sums involving the greatest integer function and Riemann-Stieltjes integration.

“…See also the papers of Hacks [24] and Berndt [2]. 3 yields a result of Kuipers [26]. 3 reduces to one of the exercises set by Eisenstein [21].…”

“…[22][23][24][25]. Kuipers pointed out in [25] and [26] that some of the results in [2] and [10] are more easily shown by using Riemann-Stieltjes integrals involving [x] rather than ((x)), and he also derived some new identities. Kuipers pointed out in [25] and [26] that some of the results in [2] and [10] are more easily shown by using Riemann-Stieltjes integrals involving [x] rather than ((x)), and he also derived some new identities.…”