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Old 2004-08-13, 01:34   #14
wblipp's Avatar
May 2003
New Haven

3·787 Posts

For those without access to Silverman and Wagstaff's paper "A Practical Analysis of Elliptical Curve Factoring," Mathematics of Computation, Vol. 61, No. 203, (July 1993), p 445-462, it defines rho(alpha) and mu(alpha, beta) as

rho(alpha) = probability largest factor of x is less than x(1/alpha)

mu(rho, alpha) = probability second largest factor of x is less than x(1/alpha)
largest factor is less than x(beta/alpha).

Rho is a commonly used version of the Dickman function, with many internet references, including Mathworld. In particular, it's known that

for 0 <= t <= 1 rho(t) = 1
for 1 <= t <= 2 rho(t) = 1-ln(t)

The pdf version of the paper (I haven't seen a print version, so this may a conversion error) then claims that mu is defined by the formula below. As explained in this thread, the forumla is wrong and does not match the tables lin the paper.
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Last fiddled with by wblipp on 2004-08-13 at 01:35
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