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 language | English |
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Pages (from-to) | 487-512 |
Journal | International Journal of Number Theory |
Volume | 13 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2017 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Arakelov
- effectivity divisor
- jump algorithm
- Poisson summation formula
- size function