On the distribution of the order and index of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>g</mml:mi><mml:mspace width="0.16em" /><mml:mo stretchy="false">(</mml:mo><mml:mi>mod</mml:mi><mml:mspace width="0.16em" /><mml:mi>p</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> over residue classes—I

Moree, Pieter

doi:10.1016/j.jnt.2004.09.004

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The Existence Of the Density Of Primes With Prescribed Index...1

Introduction1

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2006

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Cited by 9 publications

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“…The following lemma is a straightforward generalisation of [8,Lemma 6], taking into account that for every natural number n, the ratio…”

Section: The Existence Of the Density Of Primes With Prescribed Index...mentioning

confidence: 99%

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On the distribution of the order over residue classes

Moree

2006

Electron. Res. Announc. Amer. Math. Soc.

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Abstract. For a fixed rational number g ∈ {−1, 0, 1} and integers a and d we consider the set N g (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 N g (a, d) has a natural density δ g (a, d). Arithmetical properties of δ g (a, d) are described, and δ g (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 δ g (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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“…The following lemma is a straightforward generalisation of [8,Lemma 6], taking into account that for every natural number n, the ratio…”

Section: The Existence Of the Density Of Primes With Prescribed Index...mentioning

confidence: 99%

“…Felix [3]. The special case where S is an arithmetic progression was already considered by Moree [8,Thm. 5] in 2005.…”

Section: Introductionmentioning

confidence: 99%