Article ID Journal Published Year Pages File Type
4593263 Journal of Number Theory 2016 14 Pages PDF
Abstract

Let a>1a>1 be an integer. Denote by la(n)la(n) the multiplicative order of a modulo integers n. We prove that∑n≤x,(n,a)=11la(n)=Oa(xexp⁡(−(12+o(1))log⁡xlog⁡log⁡log⁡xlog⁡log⁡x)), which is an improvement over [18, Theorem 5].Further, we obtain several applications toward number fields and 2-dimensional abelian varieties of CM-type.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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