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On a distribution property of the residual order of a (mod p)—II

✍ Scribed by Leo Murata; Koji Chinen

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
267 KB
Volume
105
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let a be a positive integer which is not a perfect hth power with hX2; and Q a ðx; 4; lÞ be the set of primes ppx such that the residual order of a ðmod pÞ in Z=pZ Â is congruent to l modulo 4. When l ¼ 0; 2; it is known that calculations of xQ a ðx; 4; lÞ are simple, and we can get their natural densities unconditionally. On the contrary, when l ¼ 1; 3; the distribution properties of Q a ðx; 4; lÞ are rather complicated. In this paper, which is a sequel of our previous paper [3], under the assumption of the generalized Riemann Hypothesis, we determine completely the natural densities of xQ a ðx; 4; lÞ for l ¼ 1

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