A generalization of reduced Arakelov divisors of a number field

Let C≥1. Inspired by the LLL-algorithm, we define strongly C-reduced divisors of a number field F which are generalized from the concept of reduced Arakelov divisors. Moreover, we prove that strongly C-reduced Arakelov divisors still retain outstanding properties of the reduced ones: they form a fin...

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Bibliographic Details
Published in:Journal of number theory 2016-10, Vol.167, p.104-117
Main Author: Tran, Ha Thanh Nguyen
Format: Article
Language:English
Subjects:
Arakelov class group
Arakelov divisor
C-reduced
Infrastructure
Reduced
Strongly C-reduced
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Summary:Let C≥1. Inspired by the LLL-algorithm, we define strongly C-reduced divisors of a number field F which are generalized from the concept of reduced Arakelov divisors. Moreover, we prove that strongly C-reduced Arakelov divisors still retain outstanding properties of the reduced ones: they form a finite, regularly distributed set in the Arakelov class group and the oriented Arakelov class group of F.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2016.03.006