What question did this study set out to answer?

The aim is to derive an asymptotic formula for SL2-equivalence classes of binary quadratic forms with a specific discriminant.

May 9, 2026

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

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.

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

Key Points

Abstract

Cite This Study

Also Consider

Also Consider