Arnold's Conjectures on Weak Asymptotics and Statistics of Numerical Semigroups S(d1,d2,d3)
Leonid G. Fel
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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad