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 |x − x −1| ≤ B.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Beck, J. and Khan, M. R., On the Uniform Distribution of Inverses modulo n, Period. Math. Hungar., 44(2), 2002, 147–155.
Carmichael, R. D., The Theory of Numbers, Wiley, New York, 1914.
Estermann, T., On Kloosterman’s sums, Mathematika, 8, 1961, 83–86.
Li, S., On the Number of Elements with Maximal Order in the Multiplicative Group modulo n, Acta Arith., 86(2), 1998, 113–132.
Müller, T. and Schlage-Puchta, J-C., On the number of primitive λ-roots, Acta Arith., 115(3), 2004, 217–223.
Zheng, Z., Xia, L. and Cochrane, T., Distribution of λ-roots of composite moduli, Manuscripta Math., 2004, to appear.
(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.
About this article
Cite this article
Zheng, Z., Cochrane, T. Distribution of Primitive λ-Roots of Composite Moduli II*. Chin. Ann. Math. Ser. B 27, 549–552 (2006). https://doi.org/10.1007/s11401-005-0105-0
- Primitive roots
2000 MR Subject Classification