On a distribution property of the residual order of a (mod p)(3)

• Chinen Koji

  Department of Mathematics, Faculty of Engineering, Osaka Institute of Technology

• Murata Leo

  Department of Mathematics, Faculty of Economics, Meiji Gakuin University

書誌事項

タイトル別名

• On a distribution property of the residual order of <i>a</i> (mod <i>p</i>) — III
• On a distribution property of the residual order of a (mod p)- III

抄録

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;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 Q_a(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]).

収録刊行物

• Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ

  Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ 58 (3), 693-720, 2006

  一般社団法人 日本数学会

キーワード

• residual order
• residual index
• Artin's conjecture for primitive roots

詳細情報

• CRID: 1390282680093206784
• NII論文ID: 10018381051
• NII書誌ID: AA0070177X
• DOI: 10.2969/jmsj/1156342034
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2254407
• NDL書誌ID: 7987093
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7987093
• 本文言語コード: en
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