EAN: 9783030015107

ON THE CLASS NUMBER OF ABELIAN NUMBER FIELDS - ...

With this translation  the classic monograph Über die Klassenzahl abelscher Zahlkörper by
Helmut Hasse is now available in English for the first time. 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. 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. 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 today¿s students of and researchers in number theory.

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