Off the top of my head, the H & L conjecture should have `k-th root' in place of `square root' for polynomials of degree k. R. On Tue, 25 May 2004, Dan Asimov wrote:

Richard Guy writes:

<< ... what is significant is not the actual density over the first so many values, which clearly has to tend to zero in all cases, but the {\bf asymptotic} density, which, if we believe Hardy \& Littlewood (see {\bf A1}), is always $c\sqrt n/\ln n$, and the best that can be done \hGidx{asymptotic density} is to make the value of $c$ as large as possible. ...

...

...

Yes, that's exactly what I'm interested in -- the asymptotic behavior.

Richard: Is the Hardy-Wright asymptotic density of c sqrt(n) ^ (ln (n)) (please confirm that my parentheses are properly placed!) specifically for *quadratic* polymonials, or for *all* polynomials?

Thanks,

Dan

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