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]