Introduction of Transcendental Methods into the Arithmetic of Number Fields

  • Erich Hecke
Part of the Graduate Texts in Mathematics book series (GTM, volume 77)


In 1840, Dirichlet, in his pioneering paper “Recherches sur diverses applications de l’analyse infinitésimale à la théorie des nombres” (Crelles Journal, Vol. 19. Werke Vol. 1 p. 411), showed how the powerful methods of the analysis of continuous variables can be used in the solution of purely arithmetic problems. These methods have become of great significance for the arithmetic of number fields. Even today the problem of the class number and the problem of the distribution of prime ideals are still only approachable by these transcendental methods, and at this time they still completely evade a purely arithmetic treatment.


Prime Ideal Class Number Dirichlet Series Integral Ideal Residue Class 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Erich Hecke
    • 1
  1. 1.Department of MathematicsUniversität HamburgHamburgFederal Republic of Germany

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