5 Arnold ’ s Conjectures on Weak Asymptotics and Statistics of Numerical
نویسنده
چکیده
Three conjectures #1999–8, #1999–9 and #1999–10 which were posed by V. Arnold [2] and devoted to the statistics of the numerical semigroups are refuted for the case of semigroups generated by three positive integers d 1 , d 2 , d 3 with gcd(d 1 , d 2 , d 3) = 1. Weak asymptotics of conductor C(d 1 , d 2 , d 3) of numerical semigroup and fraction p(d 1 , d 2 , d 3) of a segment [0; C(d 1 , d 2 , d 3) − 1] occupied by semigroup are found.
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