On the Distribution of the Order over Residue Classes
نویسنده
چکیده
For a fixed rational number g ∈ {−1, 0, 1} and integers a and d we consider the set Ng(a, d) of primes p such that the order of g modulo p is congruent to a (mod d). Under the Generalized Riemann Hypothesis (GRH), it can be shown that the set Ng(a, d) has a natural density δg(a, d). Arithmetical properties of δg(a, d) are described, and δg(a, d) is compared with δ(a, d): the average density of elements in a field of prime characteristic having order congruent to a (mod d). It transpires that δg(a, d) has a strong tendency to be equal to δ(a, d), or at least to be close to it.
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تاریخ انتشار 2006