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

Publication date: 12 November 2020

Abstract: In this paper we obtain an asymptotic formula for the number of

o p e r a t o r n a m e {S L}_{2} (m a t h b b Z)

-equivalence classes of positive definite binary quadratic forms over

m a t h b b Z

having bounded discriminant

D e l t a = 1 - 4 p

, with

p

a prime. This extends work of the first named author and has an application in counting simple

(4 a + 1)

-knots of genus one.

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