An Interpretation of h, e and R indices from the Viewpoint of Riemann Zeta Function

Abstract

The h-index is an indicator, which measures both the productivity and the effect of citation of the publications for an individual scientist or scholar, journal or institution. Besides, R-Index and e-Index are also significant as h-index ignores the information of excess citation beyond h-core zone. The h-index alone conveys partial citation information, which becomes complete only when it is countered with e Index and R-Index. The h, e and R-indices are defined as the positive square roots of h-core citation, net excess citation and total citation respectively. The h-Index holds only integral values and is a discrete variable, whereas e and R-indices may have any positive value, which are continuous variables. This paper shows that the ratio of total to excess citation, i.e.(R/e)²  may be expressed as an infinite series of h-core to total citation, i.e., (R/e)²  Also, the ratio of total citation to net excess citation is explained in the light of Riemann Zeta Function (ζ(r)). It is found that only few Zeta Functions (from ζ(2) to ζ(6)) may interpret the said ratio.