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On Power Sums of Positive Numbers (1510.03420v2)
Published 11 Oct 2015 in math.CA
Abstract: In this work we establish a necessary and sufficient condition for a genus $0$ entire function $f(z)$ has only positive zeros by applying Hausdorff moment problem and Mergelyan's theorem, the obtained criterion is very much reminiscent of Xian-Jin Li's criterion on the Riemann hypothesis. We also apply this criterion to the Riemann hypothesis and the generalized Riemann hypothesis for certain Dirichlet $L$-series of real primitive characters.