New zero-free regions for the derivatives of the Riemann Zeta Function
نویسندگان
چکیده
We describe new zero-free regions for the derivatives ζ(s) of the Riemann zeta function: they take form of vertical strips in the right half-plane; and we show that the zeros located in the narrow complements of these zero-free regions – which, in analogy with the classical case, we call “critical strips” – tend to converge to their central “critical lines” and exhibit surprising vertical periodicities that enable one to give exact formulas for their number. An immediate corollary of the method is the fact that all the zeros contained inside these new critical strips are simple.
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