All Questions
5 questions
1
vote
1
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282
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Robin's inequality for odd numbers
In this article (Theorem 1.2) there is a proof for Robin's inequality for odd numbers,
$\sigma(n)/n< e^{\gamma}\log(\log(n))$ where $\gamma$ is the Euler-Mascheroni constant and $\sigma(n)$ is the ...
3
votes
0
answers
189
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Largest observed value of $S(t)$
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 ...
12
votes
0
answers
1k
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Euler's totient function and Riemann hypothesis
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 $...
17
votes
2
answers
1k
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Analogues of the Riemann zeta function that are more computationally tractable?
Many years ago, I was surprised to learn that Andrew Odlyzko does not consider the existing computational evidence for the Riemann hypothesis to be overwhelming. As I understand it, one reason is as ...
12
votes
2
answers
823
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GRH and the rank of elliptic curves
I have been using the Magma calculator recently, and while calculating ranks of elliptic curves with very big coefficients, there is a possibility to assume GRH is true, which signaficantly speeds up ...