LEADER 03443nam 22005655 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.) 225 0 $aMathematics and Statistics Series 311 08$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 LEADER 03334nam 22006615 450 001 996655267203316 005 20250430130233.0 010 $a3-031-90660-8 024 7 $a10.1007/978-3-031-90660-2 035 $a(CKB)38672342300041 035 $a(DE-He213)978-3-031-90660-2 035 $a(MiAaPQ)EBC32077043 035 $a(Au-PeEL)EBL32077043 035 $a(EXLCZ)9938672342300041 100 $a20250430d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTools and Algorithms for the Construction and Analysis of Systems $e31st International Conference, TACAS 2025, Held as Part of the International Joint Conferences on Theory and Practice of Software, ETAPS 2025, Hamilton, ON, Canada, May 3?8, 2025, Proceedings, Part III /$fedited by Arie Gurfinkel, Marijn Heule 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XXI, 269 p. 132 illus., 105 illus. in color.) 225 1 $aLecture Notes in Computer Science,$x1611-3349 ;$v15698 311 08$a3-031-90659-4 330 $aThe open access book set LNCS 15696, 15697 and 15698 constitutes the proceedings of the 31st International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2025, which was held as part of the International Joint Conferences on Theory and Practice of Software, ETAPS 2025, during May 3-8, 2025, in Hamilton, Canada. The 46 papers presented were carefully reviewed and selected from 148 submissions. The proceedings also include 14 papers from the Software Verification competition which was held as part of TACAS. The papers were organized in topical sections as follows: Part I: Program analysis, ATP and rewriting; model checking; LTL; verification; Part II: SAT and SMT solving; proofs and certificates; synthesis; equivalence checking; games; Part III: Verification; quantum and GPU; 14th Competition on Software Verification, SV-COMP 2025. 410 0$aLecture Notes in Computer Science,$x1611-3349 ;$v15698 606 $aComputer science 606 $aMicroprogramming 606 $aComputer networks 606 $aComputer simulation 606 $aSoftware engineering 606 $aTheory of Computation 606 $aControl Structures and Microprogramming 606 $aComputer Communication Networks 606 $aComputer Modelling 606 $aSoftware Engineering 615 0$aComputer science. 615 0$aMicroprogramming. 615 0$aComputer networks. 615 0$aComputer simulation. 615 0$aSoftware engineering. 615 14$aTheory of Computation. 615 24$aControl Structures and Microprogramming. 615 24$aComputer Communication Networks. 615 24$aComputer Modelling. 615 24$aSoftware Engineering. 676 $a004.0151 702 $aGurfinkel$b Arie$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aHeule$b Marijn$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996655267203316 996 $aTools and Algorithms for the Construction and Analysis of Systems$9772021 997 $aUNISA