Abstract
Let V(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 that V'(t)/t is increasing on (0, ∞). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely that V' is convex on [0, ∞). The possible relevance of the convexity of V' to the Riemann Hypothesis is discussed.
Original language | English (US) |
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Pages (from-to) | 389-399 |
Number of pages | 11 |
Journal | Constructive Approximation |
Volume | 7 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1991 |
Keywords
- AMS classification: Primary 11M26, Secondary 60K35, 82A25
- GHS inequality
- Ising model
- Lee-Yang theorem
- Riemann Hypothesis
ASJC Scopus subject areas
- Analysis
- General Mathematics
- Computational Mathematics