25 May
2004
25 May
'04
9:49 p.m.
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