Heegner number

From Free net encyclopedia

---

Current revision

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

<math>\mathbb Q(\sqrt{-n}) </math>

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:

Template:Num, Template:Num, Template:Num, Template:Num, Template:Num, Template:Num, Template:Num, Template:Num, Template:Num

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

External links

• A003173 from the On-Line Encyclopedia of Integer Sequences

Template:Numtheory-stubde:Heegner-Zahlen fr:Nombre de Heegner