| Distribution of Primitive A-Roots of Composite Moduli Ⅱ |
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| 引用本文： | Zhiyong ZHENG,Todd COCHRANE. Distribution of Primitive A-Roots of Composite Moduli Ⅱ[J]. 数学年刊B辑(英文版), 2006, 27(5): 549-552. DOI: 10.1007/s11401-005-0105-0 |
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| 作者姓名： | Zhiyong ZHENG Todd COCHRANE |
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| 摘 要： |
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| 关 键 词： | λ根 本原根 渐近公式 复合模 |
| 收稿时间： | 2005-03-28 |
Distribution of Primitive $lambda$-Roots of Composite Moduli II |
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| Zhiyong ZHENG and Todd COCHRANE. Distribution of Primitive $lambda$-Roots of Composite Moduli II[J]. Chinese Annals of Mathematics,Series B, 2006, 27(5): 549-552. DOI: 10.1007/s11401-005-0105-0 |
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| Authors: | Zhiyong ZHENG and Todd COCHRANE |
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| Affiliation: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;(2) Department of Mathematics, Kansas State University, Manhattan, Kansas 66506, USA |
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| Abstract: | Abstract 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. (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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| Keywords: | λ -Roots Primitive roots |
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