In number theory, a Heegner number is a positive integer n such that the imaginary quadratic field

$\backslash mathbb\; Q(\backslash sqrt\{-n\})$

has class number 1. Equivalently, its ring of integers has a unique factorization. The determination of such numbers is a special case of the class number problem.

According to the Stark–Heegner theorem there are precisely nine Heegner numbers:

, , , , , , , ,

This result was conjectured by Gauss and proven by Kurt Heegner in 1952.

External links

---

• A003173 from the On-Line Encyclopedia of Integer Sequences

Algebraic number theory

Heegner-Zahlen | Nombre de Heegner