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

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

2005-12-29

arxiv.org/abs/math/0512637v1

Mathematics

Number Theory

25 pages

Scientific paper

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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