Geodesic
On reduced Arakelov divisors of real quadratic fields
Ha Thanh Nguyen Tran1
1 Department of Mathematics and Systems Analysis Aalto University School of Science Otakaari 1, 02150 Espoo, Finland
Acta Arithmetica, Tome 173 (2016) no. 4, pp. 297-315.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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, similar to the properties of reduced ones. We describe an algorithm to test whether an Arakelov divisor of a real quadratic field $F$ is $C$-reduced in time polynomial in $\log|\varDelta_F|$ with $\varDelta_F$ the discriminant of $F$. Moreover, we give an example of a cubic field for which our algorithm does not work.
DOI : 10.4064/aa8007-2-2016
Keywords: generalize concept reduced arakelov divisors define c reduced divisors given number geq these c reduced divisors have remarkable properties similar properties reduced describe algorithm test whether arakelov divisor real quadratic field c reduced time polynomial log vardelta vardelta discriminant moreover example cubic field which algorithm does work

Ha Thanh Nguyen Tran 1

1 Department of Mathematics and Systems Analysis Aalto University School of Science Otakaari 1, 02150 Espoo, Finland 
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Ha Thanh Nguyen Tran. On reduced Arakelov divisors of real quadratic fields. Acta Arithmetica, Tome 173 (2016) no. 4, pp. 297-315. doi : 10.4064/aa8007-2-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8007-2-2016/

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