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

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

2002-12-16

arxiv.org/abs/math/0212220v2

Finite Fields Appl. 10 (2004), 438-463

Mathematics

Number Theory

25 pages, 4 tables. A conjecture made in the previous version is now resolved. Tables are also improved, thanks to a C++ progr

Scientific paper

10.1016/j.ffa.2003.10.001

For any prime p we consider the density of elements in the multiplicative group of the finite field F_p 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.

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