The most frequently used indicators for the productivity and impact of scientists are the total number of publication ($N_{pub}$), total number of citations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of $N_{pub}$ and $N_{cit}$. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, $N_{pub}$ and $N_{cit}$. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confimed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one characteristic for the usual socio-economic inequalities.

翻译：最常用于衡量科学家产出和影响力的指标是论文总数($N_{pub}$)、总被引次数($N_{cit}$)和Hirsch (h)指数。自2005年Hirsch的开创性论文以来，h指数是否可被视为独立于$N_{pub}$和$N_{cit}$的指标一直备受争议。利用研究者论文被引分布的帕累托形式，本文讨论了h、$N_{pub}$和$N_{cit}$之间的标度关系。分析引入了基尼指数作为被引分布的不平等度量，以及近期提出的不平等核——基尼熵（类似于熵核）。我们发现h值关于总被引次数的新的上界，该结论在Google Scholar收集的大规模数据上得到了验证。我们的分析还揭示，作者论文所获被引的个体化基尼指数峰值约为0.8，这一数值远高于通常社会经济不平等的特征值。