On the distribution of the order over residue classes
نویسندگان
چکیده
منابع مشابه
On the Distribution of the Order over Residue Classes
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 ...
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On the distribution of the order and index of g(mod p) over residue classes II
For a fixed rational number g 6∈ {−1, 0, 1} and integers a and d we consider the set Ng(a, d) of primes p for which the order of g(mod p) is congruent to a(mod d). It is shown, assuming the Generalized Riemann Hypothesis (GRH), that this set has a natural density δg(a, d). Moreover, δg(a, d) is computed in terms of degrees of certain Kummer extensions. Several properties of δg(a, d) are establi...
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For a fixed rational number g 6∈ {−1, 0, 1} and integers a and d we consider the set Ng(a, d) of primes p for which the order of g(mod p) is congruent to a(mod d). For d = 4 and d = 3 we show that, under the Generalized Riemann Hypothesis (GRH), these sets have a natural density δg(a, d) and compute it. The results for d = 4 generalise earlier work by Chinen and Murata. The case d = 3 was appar...
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For a fixed rational number g 6∈ {−1, 0, 1} and integers a and d we consider the sets Ng(a, d), respectively Rg(a, d), of primes p for which the order, respectively the index of g(mod p) is congruent to a(mod d). Under the Generalized Riemann Hypothesis (GRH), it is known that these sets have a natural density δg(a, d), respectively ρg(a, d). It is shown that these densities can be expressed as...
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ژورنال
عنوان ژورنال: Electronic Research Announcements of the American Mathematical Society
سال: 2006
ISSN: 1079-6762
DOI: 10.1090/s1079-6762-06-00168-5