On the number of binary quadratic forms having discriminant 1-4p, p prime

2020/11/12 by Miller, Alison Beth, Xiao, Stanley Yao
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.06559

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 Δ= 1-4p, with p a prime. This extends work of the first named author and has an application in counting simple (4a+1)-knots of genus one.

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