Riemann Hypothesis is equivalent to the integral equation $\int_{-\infty}^{\infty} \frac{\log \mid \zeta (1/2+it)\mid }{1+4t^2} \ dt$ =0 What does this mean? Does it mean that Riemann Hypothesis is true if and only if $\int_{-\infty}^{\infty} \frac{\log \mid \zeta (1/2+it)\mid }{1+4t^2} \ dt$ =0

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    $\begingroup$ Yes, that's what logical equivalence means. $\endgroup$ May 1, 2020 at 5:48
  • $\begingroup$ @Angina Seng Thank you $\endgroup$
    – user775902
    May 1, 2020 at 6:01

1 Answer 1


As Anginga Seng commented, to be equivalent means to be logically equivalent, i.e. one is true if and only if the other is true.


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