Assesses asymptotic behavior of binary quadratic forms with discriminant 1−4p, indicating distribution patterns.
In this paper, we obtain an asymptotic formula for the number of SL₂(Z)-equivalence classes of positive definite binary quadratic forms over Z having bounded discriminant Δ = 1-4p, with p a prime. We also give a random Euler product model for the distribution of Hurwitz class numbers, which is supported by our formula.
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Miller et al. (2026) studied this question.
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