English

Asymptotic formula for balanced words

Number Theory 2021-03-26 v1 Combinatorics Dynamical Systems

Abstract

We give asymptotic formulas for the number of balanced words whose slope α\alpha and intercept ρ\rho lie in a prescribed rectangle. They are related to uniform distribution of Farey fractions and Riemann Hypothesis. In the general case, the error term is deduced using an inequality of large sieve type.

Keywords

Cite

@article{arxiv.2103.13619,
  title  = {Asymptotic formula for balanced words},
  author = {Shigeki Akiyama},
  journal= {arXiv preprint arXiv:2103.13619},
  year   = {2021}
}
R2 v1 2026-06-24T00:32:30.598Z