On reduced Arakelov divisors of real quadratic fields
Acta Arithmetica, Tome 173 (2016) no. 4, pp. 297-315
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Ha Thanh Nguyen Tran 1
@article{10_4064_aa8007_2_2016,
author = {Ha Thanh Nguyen Tran},
title = {On reduced {Arakelov} divisors of real quadratic fields},
journal = {Acta Arithmetica},
pages = {297--315},
year = {2016},
volume = {173},
number = {4},
doi = {10.4064/aa8007-2-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8007-2-2016/}
}
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
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