On the Class Number of Abelian Number Fields

Zusatztext

<p>With this translation, the classic monograph<i>Über die Klassenzahl abelscher Zahlkörper</i> by Helmut Hasse is now available in English for the first time.</p><p>The book addresses three main topics: class number formulas for abelian number fields; expressions of the class number of real abelian number fields by the index of the subgroup generated by cyclotomic units; and the Hasse unit index of imaginary abelian number fields, the integrality of the relative class number formula, and the class number parity.</p><p>Additionally, the book includes reprints of works by Ken-ichi Yoshino and Mikihito Hirabayashi, which extend the tables of Hasse unit indices and the relative class numbers to imaginary abelian number fields with conductor up to 100.</p><p></p><p>The text provides systematic and practical methods for deriving class number formulas, determining the unit index and calculating the class number of abelian number fields. A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for todays students of and researchers in number theory.</p><p></p>

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