On a distribution property of the residual order of a (mod p) : III

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概要

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• Let a be a positive integer which is not a perfect b-th power with b≥2, q be a prime number and Qa(x;qi,j) be the set of primes p≤x such that the residual order of a (mod p) in (Z/pZ)× is congruent to j modulo qi. In this paper, which is a sequel of our previous papers [1] and [6], under the assumption of the Generalized Riemann Hypothesis, we determine the natural densities of Qa(x;qi,j) for i≥3 if q=2, i≥1 if q is an odd prime, and for an arbitrary nonzero integer j (the main results of this paper are announced without proof in [3], [7] and [2]).

• 2006-07-01

著者

• Chinen Koji

  Department Of Mathematics Faculty Of Engineering Osaka Institute Of Technology

• MURATA Leo

  Department of Mathematics, Faculty of Economics Meiji Gakuin University

• Murata Leo

  Department Of Mathematics Faculty Of Economics Meiji Gakuin University

関連論文

• On a distribution property of the residual order of a (mod p) : III
• On some fundamental relations among certain asymptotic densities

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