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Distribution of Primitive λ-Roots of Composite Moduli II*


We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q 1/2+∈. 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 λ-roots satisfying inequalities such as |xx −1| ≤ B.

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Correspondence to Zhiyong Zheng.

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(Dedicated to Professor Wang Yuan on the occasion of his 75th birthday)

*Project supported by the National Natural Science Foundation of China (No.19625102) and the 973 Project of the Ministry of Science and Technology of China.

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Zheng, Z., Cochrane, T. Distribution of Primitive λ-Roots of Composite Moduli II*. Chin. Ann. Math. Ser. B 27, 549–552 (2006).

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  • λ-Roots
  • Primitive roots

2000 MR Subject Classification

  • 11L03
  • 11L07