Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593263 | Journal of Number Theory | 2016 | 14 Pages |
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))logxlogloglogxloglogx)), which is an improvement over [18, Theorem 5].Further, we obtain several applications toward number fields and 2-dimensional abelian varieties of CM-type.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sungjin Kim,