Open AccessDistribution of Primitive λ-Roots of Composite Moduli II*
Author(s) -
Zhiyong Zheng,
Todd Cochrane
Publication year - 2006
Publication title -
chinese annals of mathematics series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.523
H-Index - 37
eISSN - 1572-9133
pISSN - 0252-9599
DOI - 10.1007/s11401-005-0105-0
Subject(s) - mathematics , moduli , distribution (mathematics) , root (linguistics) , composite number , combinatorics , pure mathematics , mathematical analysis , physics , algorithm , quantum mechanics , linguistics , philosophy
We improve estimates for the distribution of primitiveλ-roots of a composite modulus q yielding an asymptotic formula for the number of primitiveλ-roots in any interval I of length |I| >> q1/2+c. Similar results are obtained for the distribution of ordered pairs (x,x-1) with x a primitive A-root, and for the number of primitiveλ-roots satisfying inequalities such as |x - x-1| < B.
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