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Distribution of Primitive λ-Roots of Composite Moduli II

Distribution of Primitive λ-Roots of Composite Moduli II
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摘要 We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive A-roots in any interval I of length |I| 〉〉 q^1/2+ε Similar results are obtained for the distribution of ordered pairs (x, x^-1) with x a primitive λ-root, and for the number of primitive A-roots satisfying inequalities such as |x - x^-1|≤ B.
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2006年第5期549-552,共4页 数学年刊(B辑英文版)
基金 Project supported by the National Natural Science Foundation of China (No.19625102) the 973 Project of the Ministry of Science and Technology of China.
关键词 λ-Roots Primitive roots λ根 本原根 渐近公式 复合模
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参考文献6

  • 1Beck, J. and Khan, M. R., On the Uniform Distribution of Inverses modulo n, Period. Math. Hungar.,44(2), 2002, 147-155.
  • 2Carmichael, R. D., The Theory of Numbers, Wiley, New York, 1914.
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  • 4Li, S., On the Number of Elements with Maximal Order in the Multiplicative Group modulo n, Acta Arith., 86(2), 1998, 113-132.
  • 5Müller, T. and Schlage-Puchta, J-C., On the number of primitive λ-roots, Acta Arith., 115(3), 2004,217-223.
  • 6Zheng, Z., Xia, L. and Cochrane, T., Distribution of λ-roots of composite moduli, Manuscripta Math.,2004, to appear.

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