On an inequality for the Riemann zeta-function in the critical strip

Abstract

By using new power inequalities we give an elementary proof of an important relation for the Riemann zeta-function |ζ(1-s)| <= |ζ(s)| in the strip 0< Re s<1/2,\ | s| >= 12. Moreover, we establish a sufficient condition of the validity of the Riemann hypothesis in terms of the derivative with respect to Re s of |ζ(s)|2 and conjecture its necessity.

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