Abstract
In totally real number fields, we characterize the rings of S-integers (obtained by inverting a rational integer m) such that all their totally positive elements are represented as a sum of squares. We further obtain partial answers to the question: when are all the totally positive algebraic integers that are divisible by m represented as a sum of squares?.
| Original language | English |
|---|---|
| Pages (from-to) | 1145-1154 |
| Number of pages | 10 |
| Journal | NEW YORK JOURNAL OF MATHEMATICS |
| Volume | 26 |
| Publication status | Published - 2020 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- number field
- Pythagoras number
- S-integers
- Sum of squares
- Totally real