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arXiv · 1412.5043

On reduced Arakelov divisors of real quadratic fields

Ha Thanh Nguyen Tran
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Abstract

We generalize the concept of reduced Arakelov divisors and define $C$-reduced divisors for a given number $C \geq 1$. These $C$-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field $F$ is $C$-reduced in time polynomial in $\log|Δ_F|$ with $Δ_F$ the discriminant of $F$. Moreover, we give an example of a cubic field for which our algorithm does not work.

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Ha Thanh Nguyen Tran. 2016-05-25. On reduced Arakelov divisors of real quadratic fields. https://doi.org/10.4064/aa8007-2-2016

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