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I am looking for an upper-bound of the Euler's totient function $\varphi$ which would be equivalent to the Riemann hypothesis (RH). There is the following Nicolas' criterion about primorial numbers $...

Let $S(t)$ be the deviation of the number of zeros of the Riemann zeta function up to height $t$ from the expectation. What is the largest observed value of $S(t)$ today? Here is a quote from a ...