On a generalization of Artin's Conjecture to composite moduli


Wentang Kuo

13:30:00 - 14:30:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

For a given non-zero integer a other than 1, -1, or a perfect square, Artin's primitive root conjecture is about the density of primes p for which a is a primitive root of the multiplicative group of integers modulo p. Li and Pomerance formulated and proved an analogue of this conjecture to composite moduli. More precisely, let N_a(x) be the number of positive integers n less or equal x such that (a,n)=1 and a generates the largest cyclic subgroup of the multiplicative group of integers modulo n. They showed that
lim sup N_a(x)/x = 0, and lim inf N_a(x)/x >0.

In this talk, we will prove a Carlitz module analogue of Li and Pomerance's results. This is a joint work with E. Eisenstein, A. Felix, L. Jain, X. Li, and Y.-R. Liu.

For material related to this talk, click here.