Abstract
A positive definite integral quadratic form is said to be almost (primitively) universal if it (primitively) represents all but at most finitely many positive integers. In general, almost primitive universality is a stronger property than almost universality. The two main results of this paper are (1) every primitively universal form nontrivially represents zero over every ring \(\mathbb {Z}_p\) of p-adic integers, and (2) every almost universal form in five or more variables is almost primitively universal.
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Notes
Note that our convention for the indexing of the components differs from that of [10].
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Earnest, A.G., Gunawardana, B.L.K. On locally primitively universal quadratic forms. Ramanujan J 55, 1145–1163 (2021). https://doi.org/10.1007/s11139-020-00305-7
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DOI: https://doi.org/10.1007/s11139-020-00305-7