Minimal rank of primitively n-universal integral quadratic forms over local rings
Abstract
Abstract Let F be a local field and let R be its ring of integers. For a positive integer n , an integral quadratic form defined over R is called primitively n -universal if it primitively represents all quadratic forms of rank n . It was proved in [7] that the minimal rank of primitively 1-universal quadratic forms over the p -adic integer ring $$\mathbb {Z}_p$$ Z p is 2 if p is odd, and 3 otherwise. In this article, we completely determine the minimal rank of primitively n -universal quadratic forms over R for any positive integer n and any local ring R such that 2 is a unit or a prime.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Coding theory and cryptography
Publication details
- Journal / source
- The Ramanujan Journal
- Publisher
- Springer Science and Business Media LLC
- Volume
- 71
- Issue
- 1
- Publication date
- 24 August 2026
- Language
- EN