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I am interested to know the largest computed summatory liouville interval, an implementation of which is detailed in Section 4.1 of [1].

The wikipedia page [2] for the function charts summatory liouville up to an interval of 10$^7$. I would like to know the largest computed summatory liouville value. Where might be the best reference to find this out?

1 -

2 -


-- Rob

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To the best of my knowledge, the furthest $L(x)$ has been calculated up to is $x = 2 \cdot 10^{14}$, as reported in this paper: Out of curiosity, may I ask why you are interested in this summatory function? – Peter Humphries May 15 '12 at 10:36
Peter, Many thanks. I have a parallel code implementation of summatory liouville, and having gone through that paper, I am able to verify the reported L(x) values. Perhaps one could tell me what value I may be able to offer by calculating L(x) for something greater than $2 \cdot 10^{14}$ .. perhaps $3.5 \cdot 10^{14}$ ? I have available to me a 32 node cluster of 8 core machines – Rob May 15 '12 at 16:23
See this question (and non-answer):… – Stopple May 15 '12 at 18:03

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