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Old 2004-08-13, 01:34   #14
wblipp
 
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"William"
May 2003
New Haven

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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)
AND
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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