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Arnold's Conjectures on Weak Asymptotics and Statistics of Numerical Semigroups S(d1,d2,d3)

Leonid G. Fel

math.NTarXiv:math/0512637

Abstract

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 d1,d2,d3 with gcd(d1,d2,d3)=1. Weak asymptotics of conductor C(d1,d2,d3) of numerical semigroup and fraction p(d1,d2,d3) of a segment [0;C(d1,d2,d3)-1] occupied by semigroup are found.

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