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OverviewWith 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. Full Product DetailsAuthor: Helmut Hasse , Mikihito HirabayashiPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2019 Dimensions: Width: 15.50cm , Height: 2.40cm , Length: 23.50cm Weight: 0.770kg ISBN: 9783030015107ISBN 10: 3030015106 Pages: 365 Publication Date: 08 May 2019 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Language: English Table of ContentsPart I.- Introduction.- The Generalized Class Number Formulas.- The Arithmetic Structure of the Class Number Formula for Real Fields.- The Arithmetic Structure of the Relative Class Number Formula for Imaginary Fields.- Appendix: Tables of Relative Class Numbers - Part II.- On the Relative Class Number of the Imaginary Abelian Number Field I.- On the Relative Class Number of the Imaginary Abelian Number Field II.- Supplemental Readings.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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