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May 9, 2026The Quarterly Journal of Mathematics0 citations

On the Number of Binary Quadratic Forms Having Discriminant 1 − 4 p, p Prime

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AMAlison Beth MillerSXStanley Yao Xiao

Key Points

  • The aim is to derive an asymptotic formula for SL2-equivalence classes of binary quadratic forms with a specific discriminant.
  • Derived an asymptotic formula for the number of positive definite binary quadratic forms
  • Analyzed equivalence classes within SL2(Z)
  • Explored Hurwitz class number distributions using a random Euler product model.
  • Provided an asymptotic formula relating to the number of classes with discriminant 1−4p
  • Demonstrated the effectiveness of the random Euler product model in describing Hurwitz class numbers.

Abstract

ABSTRACT 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 = 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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Cite This Study

Miller et al. (2026) studied this question.

synapsesocial.com/papers/69fed03cb9154b0b8287740bhttps://doi.org/10.1093/qmath/haag009
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