On the average number of elements in a finite field with order or index in a prescribed residue class

الأصل · EN

For any prime p we consider the density of elements in the multiplicative group of the finite field Fₚ having order, respectively index, congruent to a(mod d). We compute these densities on average, where the average is taken over all finite fields of prime order. Some connections between the two densities are established. It is also shown how to compute these densities with high numerical accuracy.