The GHS inequality and the Riemann hypothesis

Charles M. Newman

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)389-399
Number of pages11
JournalConstructive Approximation
Issue number1
StatePublished - Dec 1991


  • 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


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