The GHS inequality and the Riemann hypothesis |
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Authors: | Charles M Newman |
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Institution: | 1. Department of Mathematics, University of Arizona, 85721, Tucson, Arizona, USA
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Abstract: | LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4
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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.Communicated by Richard Varga. |
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Keywords: | AMS classification" target="_blank">AMS classification Primary 11M26 Secondary 60K35 82A25 |
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