Open AccessA Simple Proof of Siegel's Theorem
Author(s) -
Dorian Goldfeld
Publication year - 1974
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.71.4.1055
Subject(s) - simple (philosophy) , mathematical proof , mathematics , class (philosophy) , algebraic number , analytic proof , combinatorics , combinatorial proof , discrete mathematics , calculus (dental) , computer science , mathematical analysis , philosophy , medicine , dentistry , geometry , epistemology , artificial intelligence
A brief and simple proof of Siegel's celebrated theorem thath(d) »d 1/2-[unk] , asd → ∞, is given. Hereh(d) denotes the class number of the quadratic fieldQ ([unk]-d ). Simple proofs that do not make use of algebraic number theory have been previously given by Estermann and Chowla.