Back to Search
Start Over
Indecomposable integers in real quadratic fields.
- Source :
-
Journal of Number Theory . Jul2020, Vol. 212, p458-482. 25p. - Publication Year :
- 2020
-
Abstract
- In 2016, Jang and Kim stated a conjecture about the norms of indecomposable integers in real quadratic number fields Q (D) where D > 1 is a squarefree integer. Their conjecture was later disproved by Kala for D ≡ 2 mod 4. We investigate such indecomposable integers in greater detail. In particular, we find the minimal D in each congruence class D ≡ 1 , 2 , 3 mod 4 that provides a counterexample to the Jang-Kim Conjecture; provide infinite families of such counterexamples; and state a refined version of the Jang-Kim Conjecture. Lastly, we prove a slightly weaker version of our refined conjecture that is of the correct order of magnitude, showing the Jang-Kim Conjecture is only wrong by at most O (D). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 212
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 142424607
- Full Text :
- https://doi.org/10.1016/j.jnt.2019.11.005