Computing dimensions of spaces of Arakelov divisors of number fields
Number Theory
2016-09-12 v2
Abstract
The function for a number field is analogous to the dimension of the Riemann-Roch spaces at divisors on an algebraic curve. We provide a method to compute this function for number fields with unit group of rank at most 2, even with large discriminant. This method is based on using LLL-reduced bases, the "jump algorithm" and Poisson summation formula.
Keywords
Cite
@article{arxiv.1506.04540,
title = {Computing dimensions of spaces of Arakelov divisors of number fields},
author = {Ha Thanh Nguyen Tran},
journal= {arXiv preprint arXiv:1506.04540},
year = {2016}
}