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Thursday, March 1, 2018

**Abstract:** In this talk, we discuss some monotonicity results for a class of Dirichlet series. The fact that $\zeta'(s)$ is in that class presents a first example of an arithmetic function for which the associated Dirichlet series is completely monotonic, but not logarithmically completely monotonic. Moreover, we will see how our methods give rise to another formulation of the Riemann Hypothesis for the L-function associated to the Ramanujan-tau function. Based on joint work with S. Chaubey and A. Zaharescu.