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Failures of integral Springer's Theorem
- Publication Year :
- 2024
-
Abstract
- We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed.<br />Comment: preprint, 10 pages
- Subjects :
- Mathematics - Number Theory
11E12, 11H55, 11R80
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.12844
- Document Type :
- Working Paper