We generalize the concept of reduced Arakelov divisors and define C-reduced divisors for a given number C ≥ 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 with the discriminant of F. Moreover, we give an example of a cubic field for which our algorithm does not work.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8007-2-2016,
author = {Ha Thanh Nguyen Tran},
title = {On reduced Arakelov divisors of real quadratic fields},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {297-315},
zbl = {06602743},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8007-2-2016}
}
Ha Thanh Nguyen Tran. On reduced Arakelov divisors of real quadratic fields. Acta Arithmetica, Tome 172 (2016) pp. 297-315. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8007-2-2016/