The Stark-Heegner Theorem identifies the exact nine positive whole numbers d for which the ring of integers of the imaginary quadratic field generated by the square root of negative d has unique factorization, equivalently has class number one: 1, 2, 3, 7, 11, 19, 43, 67 and 163. Proved by Kurt Heegner in 1952 in a proof initially doubted on a technical point later confirmed correct, and independently by Harold Stark and by Alan Baker, it resolved Gauss's longstanding class number one problem for imaginary quadratic fields.
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Source Stark-Heegner theorem (Wikipedia)
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Source Stark-Heegner theorem (Wikipedia)
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1. Wikipedia: Stark-Heegner theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
The class number of Q ( d ) ({\sqrt {d}})} is one if and only if the ring of integers of Q ( d ) ({\sqrt {d}})} is a principal ideal domain.
2. Stark-Heegner theorem (Wikipedia)
History section
Harold Stark published a proof in 1967
In Branch: Number Theory, Lead sentence
In number theory, the Heegner theorem or Stark-Heegner theorem establishes the complete list of the quadratic imaginary number fie
Proved By: Kurt Heegner, Lead
It was essentially proven by Kurt Heegner in 1952, but Heegner's proof was not accepted until an academic mathematician Harold Stark published a proof in 1967 which had many commonalities to Heegner's work, though Stark considers the proofs to be different.
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