Diagonal odd-regular ternary quadratic forms
Mingyu Kim

TL;DR
This paper classifies diagonal odd-regular ternary quadratic forms, showing there are at most 147 such forms and confirming the odd-regularity of all but six candidates, advancing understanding of quadratic form representations.
Contribution
It provides a finite classification of diagonal odd-regular ternary quadratic forms and verifies their odd-regularity for nearly all candidates, which was previously unknown.
Findings
Maximum of 147 diagonal odd-regular ternary quadratic forms.
Odd-regularity confirmed for all but 6 candidates.
Progress in classifying quadratic forms based on local representation.
Abstract
A (positive definite primitive integral) quadratic form is called odd-regular if it represents every odd positive integer which is locally represented. In this paper, we show that there are at most 147 diagonal odd-regular ternary quadratic forms and prove the odd-regularities of all but 6 candidates.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Analytic Number Theory Research · Finite Group Theory Research
