# Questions tagged [riemann-hypothesis]

Questions on the Riemann hypothesis, a conjecture on the behavior of the complex zeros of the Riemann $\zeta$ function. You might want to add the tag [riemann-zeta] to your question as well.

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### Questions on a formula for the Mertens function

The Mertens function $M(x)$ is defined as follows. (1) $\quad M(x)=\sum\limits_{n=1}^x\mu(n)$ I've noticed the Merten's function can also be evaluated as follows which is related to OEIS entry ...
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### What is the size of the kth Superabundant Number?

Utilizing the data generated by T.D. Noe for the first $10^6$ terms of A004394, a plot of $k$ against $log_{10}(S(k))$ where S(K) is the $k^{th}$ Superabundant Number shows a strong linear ...
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### Riemann Hypothesis and Complex modular exponentiation [on hold]

I have always liked this graph. It looks like modular arithmetic in the 12-hour clock. Is there any relationship of congruence of complex exponents in the critical line? to know the behavior of this ...
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### What approach provides the largest known verification of the Riemann Hypothesis?

The Riemann Hypothesis is true if and only if Robin's Inequality is true for all n>5040. It has also been shown by Akbary and Friggstad that the smallest counterexample greater than 5040, if it exists,...
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### zeta of imaginary numbers

So the riemman hypothesis was dealing with the real part of the s be 1/2 and I was wondering if it is possible to take zeta of imaginary numbers and if it is, how would you proceed to do so?
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### The connection between the Riemann hypothesis and the harmonic series

I have heard most people say that the harmonic series, given by $\displaystyle\sum_{n=1}^{\infty}{n^{-1}}$, is central or somehow related to a proof of the Riemann hypothesis. I have been trying to ...
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