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arXiv · 1505.02279

A generalization of reduced Arakelov divisors of a number field

Ha Thanh Nguyen Tran
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Abstract

Let $C \geq 1$. 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 $F$.

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Ha Thanh Nguyen Tran. 2016-05-25. A generalization of reduced Arakelov divisors of a number field. https://doi.org/10.1016/j.jnt.2016.03.006

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