Computing dimensions of spaces of Arakelov divisors of number fields

Ha Tran Nguyen Thanh

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

The function (Formula presented.) 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.

Original languageEnglish
Pages (from-to)487-512
JournalInternational Journal of Number Theory
Volume13
Issue number2
DOIs
Publication statusPublished - Mar 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Arakelov
  • effectivity divisor
  • jump algorithm
  • Poisson summation formula
  • size function

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