Open Access
July, 2006 On a distribution property of the residual order of a (mod p)- III
Koji CHINEN, Leo MURATA
J. Math. Soc. Japan 58(3): 693-720 (July, 2006). DOI: 10.2969/jmsj/1156342034

Abstract

Let a be a positive integer which is not a perfect b -th power with b 2 , q be a prime number and Q a ( x ; q i , j ) be the set of primes p x such that the residual order of a ( m o d p ) in ( Z / p Z ) × is congruent to j modulo q i . 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 Q a ( x ; q i , 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]).

Citation

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Koji CHINEN. Leo MURATA. "On a distribution property of the residual order of a (mod p)- III." J. Math. Soc. Japan 58 (3) 693 - 720, July, 2006. https://doi.org/10.2969/jmsj/1156342034

Information

Published: July, 2006
First available in Project Euclid: 23 August 2006

zbMATH: 1102.11002
MathSciNet: MR2254407
Digital Object Identifier: 10.2969/jmsj/1156342034

Subjects:
Primary: 11A07
Secondary: 11N05 , 11N25

Keywords: Artin's conjecture for primitive roots , residual index , residual order

Rights: Copyright © 2006 Mathematical Society of Japan

Vol.58 • No. 3 • July, 2006
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