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Minimal universality criterion sets on the representations of binary quadratic forms
Cited 3 time in
Web of Science
Cited 3 time in Scopus
- Authors
- Issue Date
- 2022-09
- Publisher
- Academic Press
- Citation
- Journal of Number Theory, Vol.238, pp.37-59
- Abstract
- © 2021 Elsevier Inc.For a set S of (positive definite and integral) quadratic forms with bounded rank, a quadratic form f is called S-universal if it represents all quadratic forms in S. A subset S0 of S is called an S-universality criterion set if any S0-universal quadratic form is S-universal. We say S0 is minimal if there does not exist a proper subset of S0 that is an S-universality criterion set. In this article, we study various properties of minimal universality criterion sets. In particular, we show that for most binary quadratic forms f, minimal S-universality criterion sets are unique in the case when S is the set of all subforms of the binary form f.
- ISSN
- 0022-314X
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