On a distribution property of the residual order of <i>a</i> (mod <i>p</i>) — III
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- Chinen Koji
- Department of Mathematics, Faculty of Engineering, Osaka Institute of Technology
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- Murata Leo
- Department of Mathematics, Faculty of Economics, Meiji Gakuin University
Bibliographic Information
- Other Title
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- On a distribution property of the residual order of a (mod p)(3)
- On a distribution property of the residual order of a (mod p)- III
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Description
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]).
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 58 (3), 693-720, 2006
The Mathematical Society of Japan
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Details 詳細情報について
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- CRID
- 1390282680093206784
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- NII Article ID
- 10018381051
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- MRID
- 2254407
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- NDL BIB ID
- 7987093
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed