Equivalences to the Riemann Hypothesis

The Riemann Hypothesis has been shown to be equivalent to an astounding variety of statements in several different areas of mathematics. Some of those equivalences are nearly trivial. For example, RH is equivalent to the nonvanishing of $\zeta(s)$ in the half-plane $\sigma>\frac12$. Other equivalences appear surprizing and deep. Examples of both kinds are collected below.

The results in the following articles will eventually find their way here:

[ MR 96g:11111] [ MR 98f:11113] [ MR 96a:11085] [ MR 95c:11105] [ MR 94i:58155] [ MR 89j:15029] [ MR 87b:11084]

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