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| Distribution of Primitive $\lambda$-Roots of Composite Moduli II |
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Citation： |
Zhiyong ZHENG,Todd COCHRANE.Distribution of Primitive $\lambda$-Roots of Composite Moduli II[J].Chinese Annals of Mathematics B,2006,27(5):549~552 |
| Page view： 1087
Net amount： 863 |
Authors： |
Zhiyong ZHENG; Todd COCHRANE |
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| Abstract： |
We improve estimates for the distribution of primitive
$\lambda$-roots of a composite modulus $q$ yielding an asymptotic
formula for the number of primitive $\lambda$-roots in any
interval $I$ of length $|I| \gg q^{\frac 12 + \epsilon}$. Similar
results are obtained for the distribution of ordered pairs
$(x,x^{-1})$ with $x$ a primitive $\lambda$-root, and for the
number of primitive $\lambda$-roots satisfying inequalities such
as $|x -x^{-1}|\le B$. |
Keywords： |
$\lambda$-Roots, Primitive roots |
Classification： |
11L03, 11L07 |
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