English

Quartic and Octic Characters Modulo n

Number Theory 2016-03-28 v3

Abstract

The average number of primitive quadratic Dirichlet characters of modulus n tends to a constant as n->infty. The same is true for primitive cubic characters. It is therefore surprising that, as n->infty, the average number of primitive quartic characters of modulus n grows with ln(n), and that the average number of primitive octic characters of modulus n grows with ln(n)^2. Leading coefficients in the asymptotic expressions are also computed.

Cite

@article{arxiv.0907.4894,
  title  = {Quartic and Octic Characters Modulo n},
  author = {Steven Finch},
  journal= {arXiv preprint arXiv:0907.4894},
  year   = {2016}
}

Comments

13 pages; updated reference [11] and added reference [12]

R2 v1 2026-06-21T13:29:56.102Z