Quartic and Octic Characters Modulo n

Details Quartic and Octic Characters Modulo n Quartic and Octic Characters Modulo n

2009-07-28

arxiv.org/abs/0907.4894v2

Mathematics

Number Theory

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

Scientific paper

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.

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