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Universal quadratic forms and Dedekind zeta functions
- Publication Year :
- 2023
-
Abstract
- We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields.<br />Comment: 12 pages. Preprint
- Subjects :
- Mathematics - Number Theory
11E12, 11E20, 11H06
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2311.12911
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S1793042124500908