Abstract
In this paper, we deal with the link between fractional calculus, Riemann zeta functions and prime numbers. In particular, we compute the logarithmic fractional derivative of the Riemann zeta function. In addition, we study the possibility to express ζ(α)(s) as an Euler product. This leads us to generalize the Euler’s product formula for Dirichlet series where the hypothesis of multiplicative function is replaced by a homomorphism.
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