PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On reduced Arakelov divisors of real quadratic fields

Volume 173 / 2016

Ha Thanh Nguyen Tran Acta Arithmetica 173 (2016), 297-315 MSC: Primary 11Y16; Secondary 11Y40. DOI: 10.4064/aa8007-2-2016 Published online: 1 June 2016

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, 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.

Authors

  • Ha Thanh Nguyen TranDepartment of Mathematics and Systems Analysis
    Aalto University School of Science
    Otakaari 1, 02150 Espoo, Finland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image