The GHS inequality and the Riemann hypothesis |
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Authors: | Charles M. Newman |
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Affiliation: | 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– 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: | KeywordHeading" >AMS classification Primary 11M26 Secondary 60K35 82A25 |
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