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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 - http://www.macs.hw.ac.uk/~greg/publications/atamhb.damp09.pdf

2 - http://en.wikipedia.org/wiki/Liouville_function

Best,

-- Rob

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  • $\begingroup$ 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: davidson.edu/math/mossinghoff/liouvillesums2_bfm.pdf. Out of curiosity, may I ask why you are interested in this summatory function? $\endgroup$
    – Peter Humphries
    Commented May 15, 2012 at 10:36
  • $\begingroup$ 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 $\endgroup$
    – Rob
    Commented May 15, 2012 at 16:23
  • $\begingroup$ See this question (and non-answer): mathoverflow.net/questions/75168/… $\endgroup$
    – Stopple
    Commented May 15, 2012 at 18:03
  • $\begingroup$ @Peter Humphries - Actually, I would be interested in this, but the link you provide seems broken. Would you have a replacement for it? $\endgroup$
    – EGME
    Commented Nov 15, 2022 at 14:55
  • $\begingroup$ ams.org/journals/mcom/2008-77-263/S0025-5718-08-02036-X $\endgroup$
    – Peter Humphries
    Commented Nov 15, 2022 at 16:50

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