Talk:Jeffrey Lagarias

Robin's inequality
The following result is due to Robin (1984): The Riemann Hypothesis is true if and only if $$ \sigma(n) < e^{\gamma} n \log \log n $$ for all $$ n > 6000 $$

Lagarias's inequality (2002) is a minor variation on Robin's inequality as reading his proof reveals.

Therefore it would seem appropriate to mention this inequality only in passing, as a minor side-note. Not as Lagarias's main achievement. Indeed the way things are phrased now they are insulting to both Lagarias and Robin. To Lagarias because this inequality is far from his main achievement. To Robin, because he deserves a large part of the credit but his name appears nowhere. Indeed, the situation also makes Lagarias look dishonest (although, I am in no way suggesting he is dishonest).

I hope fellow Wikipedians understand why I am uneasy with the current state of affairs. — Preceding unsigned comment added by 128.12.220.20 (talk) 09:55, 28 November 2011 (UTC)

Equivalent
I believe Lagarias' equivalent harmonic form can be manipulated to requiring

$$e(AQ)<=e(Hn)*ln(Hn)$$

where  ln(sigma(n)) <= A*Q(n)+ B    with B<=ln(2),H(n)=harmonic # and Q(n)=harmonic(n/2) ie half-harmonic

strict proof requires A<=1.0 (B=ln(2)). Actual numerics appear to show zero-intercept slopes for HCN>=7207200 all<A, so within bounds (comment copied from another Talk page)--Billymac00 (talk) 00:29, 2 July 2008 (UTC)

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