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<p>In this paper, for each integral quadratic ternary form <i>Q</i> with prescribed Jordan decomposition over the ring <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {Z}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>, where <i>p</i> is odd, we give criteria for determining whether there exists a primitive representation of integers <i>A</i> with <i>p</i>-valuation at most three by the form <i>Q</i>. As an application of the local criteria, we prove a result related to primitive prime-universality and primitive odd-universality.</p>

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Local description of primitive representations by ternary quadratic forms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月12日

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  • Natalia Budarina

摘要

In this paper, for each integral quadratic ternary form Q with prescribed Jordan decomposition over the ring \(\mathbb {Z}_p\) Z p , where p is odd, we give criteria for determining whether there exists a primitive representation of integers A with p-valuation at most three by the form Q. As an application of the local criteria, we prove a result related to primitive prime-universality and primitive odd-universality.