Abstract
LetV(t) be the even function on (−∞, ∞) which is related to the Riemann xi-function by Ξ(x/2)=4∫ ∞−∞ exp(ixt−V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ∞). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ∞). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.
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Communicated by Richard Varga.
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Newman, C.M. The GHS inequality and the Riemann hypothesis. Constr. Approx 7, 389–399 (1991). https://doi.org/10.1007/BF01888165
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DOI: https://doi.org/10.1007/BF01888165