LEADER 03393nam 22005535 450 001 9910338259503321 005 20251116212323.0 010 $a3-030-01512-2 024 7 $a10.1007/978-3-030-01512-1 035 $a(CKB)4100000007992537 035 $a(DE-He213)978-3-030-01512-1 035 $a(MiAaPQ)EBC5755795 035 $a(Au-PeEL)EBL5755795 035 $a(OCoLC)1099336326 035 $a(PPN)235670723 035 $a(EXLCZ)994100000007992537 100 $a20190423d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOn the Class Number of Abelian Number Fields $eExtended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi /$fby Helmut Hasse 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XXXVIII, 365 p. 33 illus.) 311 08$a3-030-01510-6 327 $aPart 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. 330 $aWith 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. 606 $aNumber theory 606 $aAlgebra 606 $aField theory (Physics) 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 615 0$aNumber theory. 615 0$aAlgebra. 615 0$aField theory (Physics) 615 14$aNumber Theory. 615 24$aField Theory and Polynomials. 676 $a512.7 676 $a512.86 700 $aHasse$b Helmut$4aut$4http://id.loc.gov/vocabulary/relators/aut$040862 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338259503321 996 $aOn the Class Number of Abelian Number Fields$91733477 997 $aUNINA