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

“…Using Theorem 2 of [6] such Euler products can be expressed in terms of values at integer points of the (partial) Riemann zeta-function. This enables one to evaluate these constants with hunderds of decimals of precision, see [13]. A similar idea forms the basis of Theorem 6 and Theorem 7.…”

“…Since the Artin constant (see e.g. [13]) and L(2, χ), L(3, χ) and L(4, χ) can be each evaluated with high numerical accuracy, Theorem 6 allows one to compute A χ with high numerical accuracy. Using Proposition 6 and part 7 of Theorem 1, ρ(a, d), respectively δ(a, d), can then be evaluated with high numerical precision.…”