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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1974 Apr;71(4):1055. doi: 10.1073/pnas.71.4.1055

A Simple Proof of Siegel's Theorem

Dorian M Goldfeld 1
PMCID: PMC388160  PMID: 16592152

Abstract

A brief and simple proof of Siegel's celebrated theorem that h(d) » d1/2-[unk], as d → ∞, is given. Here h(d) denotes the class number of the quadratic field Q([unk]-d). Simple proofs that do not make use of algebraic number theory have been previously given by Estermann and Chowla.

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