On reduced Arakelov divisors of real quadratic fields

Ha Thanh Nguyen Tran. "On reduced Arakelov divisors of real quadratic fields." Acta Arithmetica 173.4 (2016): 297-315. <http://eudml.org/doc/286245>.

@article{HaThanhNguyenTran2016,
abstract = {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 $log|Δ_\{F\}|$ with $Δ_\{F\}$ the discriminant of F. Moreover, we give an example of a cubic field for which our algorithm does not work.},
author = {Ha Thanh Nguyen Tran},
journal = {Acta Arithmetica},
keywords = {Arakelov divisor; reduced},
language = {eng},
number = {4},
pages = {297-315},
title = {On reduced Arakelov divisors of real quadratic fields},
url = {http://eudml.org/doc/286245},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Ha Thanh Nguyen Tran
TI - On reduced Arakelov divisors of real quadratic fields
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 4
SP - 297
EP - 315
AB - 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 $log|Δ_{F}|$ with $Δ_{F}$ the discriminant of F. Moreover, we give an example of a cubic field for which our algorithm does not work.
LA - eng
KW - Arakelov divisor; reduced
UR - http://eudml.org/doc/286245
ER -