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.