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This is a Quantitative Study study.

September 30, 2025Open Access

Local description of primitive representations by ternary quadratic forms

Key Points

Criteria for identifying primitive representations of integers are presented.
The study focuses on integral quadratic forms with prescribed Jordan decomposition over the local field.
Results include connections to both primitive prime-universality and primitive odd-universality.
Applications enhance the understanding of representations in number theory, particularly in local fields.

Abstract

Abstract In this paper, for each integral quadratic ternary form Q with prescribed Jordan decomposition over the ring Zₚ 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.

Local description of primitive representations by ternary quadratic forms

Key Points

Abstract

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