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Re: Spencer-Brown's purported proof of Riemann Hypothesis
Posted:
Aug 6, 2006 6:30 AM
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In article <je2dnSC6K7IEWVbZnZ2dnUVZ_qWdnZ2d@comcast.com>,
Tim Peters <tim.one@comcast.net> wrote:
>Note: because it's never clear, I'll note that by "li(n)" he must mean the
>integral from 0 (not 2) to n of 1/log(t) dt.
That's right; in a long footnote on beginning on page 7 he complains
about "false values" of li(n) "obtained by beginning the integration
in the wrong place (at 2 instead of 0)". It's fun to read.
He seems to make no attempt at all to prove his strong bound
|pi(n) - li(n)| < |sqrt(li n)| for n > 1
except to claim that it follows from the Tschebycheff-Sylvester
formula
.95695 (n/log n) < pi(n) < 1.0443 (n/log n)
I have no idea why thinks so. The T-S formula bounds pi(n) to
within errors of O(n/log n), but to get the Riemann hypothesis
one needs bounds with errors of O(sqrt(n) log(n)).
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