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Arnold's Conjectures on Weak Asymptotics and Statistics of Numerical Semigroups S(d_1,d_2,d_3)

Leonid G. Fel
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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 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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Leonid G. Fel. 2005-12-29. Arnold's Conjectures on Weak Asymptotics and Statistics of Numerical Semigroups S(d_1,d_2,d_3). https://arxiv.org/abs/math/0512637

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