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Volumn 349, Issue 9, 1997, Pages 3657-3678

The class number one problem for some non-abelian normal CM-fields

Author keywords

CM field; Dihedral field; Relative class number

Indexed keywords


EID: 21944444366     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01768-6     Document Type: Article
Times cited : (28)

References (26)
  • 1
    • 0040574158 scopus 로고
    • The imaginary bicyclic biquadratic fields with class number 1
    • BP MR 49:4974
    • [BP] E. Brown and C.J. Parry. The imaginary bicyclic biquadratic fields with class number 1. J. Reine Angew. Math. 266 (1974), 118-120. MR 49:4974
    • (1974) J. Reine Angew. Math. , vol.266 , pp. 118-120
    • Brown, E.1    Parry, C.J.2
  • 2
    • 0007425307 scopus 로고
    • On the imaginary bicyclic biquadratic fields with class number 2
    • BWW MR 56:305
    • [BWW] D.A. Buell, H.C. Williams and K.S. Williams. On the imaginary bicyclic biquadratic fields with class number 2. Math. Comp. 31 (1977), 1034-1042. MR 56:305
    • (1977) Math. Comp. , vol.31 , pp. 1034-1042
    • Buell, D.A.1    Williams, H.C.2    Williams, K.S.3
  • 5
    • 0002865488 scopus 로고
    • Some analytic bounds for zeta functions and class numbers
    • Hof MR 80k:12019
    • [Hof] J. Hoffstein. Some analytic bounds for zeta functions and class numbers. Inventiones Math. 55 (1979), 37-47. MR 80k:12019
    • (1979) Inventiones Math. , vol.55 , pp. 37-47
    • Hoffstein, J.1
  • 6
    • 51249161846 scopus 로고
    • On a ratio between relative class number
    • Hor MR 94a:11171
    • [Hor] K. Horie. On a ratio between relative class number. Math. Z. 211 (1992), 505-521. MR 94a:11171
    • (1992) Math. Z. , vol.211 , pp. 505-521
    • Horie, K.1
  • 7
    • 0344414743 scopus 로고
    • p as Galois group
    • JY MR 84g:12011
    • p as Galois group. J. Number Th. 15 (1982), 347-375. MR 84g:12011
    • (1982) J. Number Th. , vol.15 , pp. 347-375
    • Jensen, C.U.1    Yui, N.2
  • 8
    • 0007452103 scopus 로고
    • Continued fractions and real quadratic fields
    • Lou 1 MR 90a:11119
    • [Lou 1] S. Louboutin. Continued fractions and real quadratic fields. J. Number Theory 30 (1988), 167-176. MR 90a:11119
    • (1988) J. Number Theory , vol.30 , pp. 167-176
    • Louboutin, S.1
  • 9
    • 0039605770 scopus 로고
    • Norme relative de l'unité fondamentale et 2-rang du groupe des classes d'idéaux de certains corps biquadratiques
    • Lou 2 MR 93a:11090
    • [Lou 2] S. Louboutin. Norme relative de l'unité fondamentale et 2-rang du groupe des classes d'idéaux de certains corps biquadratiques. Acta Arith. 58 (1991), 273-288. MR 93a:11090
    • (1991) Acta Arith. , vol.58 , pp. 273-288
    • Louboutin, S.1
  • 10
    • 0010823370 scopus 로고
    • S. Louboutin. Calcul des nombres de classes relatifs de certains corps de classes de Hilbert
    • Lou 3 MR 95g:11111
    • [Lou 3] S. Louboutin. Calcul des nombres de classes relatifs de certains corps de classes de Hilbert. C. R. Acad. Sci. Paris Sér. I Math. 319 I (1994), 321-325. MR 95g:11111
    • (1994) C. R. Acad. Sci. Paris Sér. I Math. , vol.319 I , pp. 321-325
  • 11
    • 84972577236 scopus 로고
    • Calcul du nombre de classes des corps de nombres
    • Lou 4 MR 97a:11176
    • [Lou 4] S. Louboutin. Calcul du nombre de classes des corps de nombres. Pacific J. Math. 17 (1995), 455-467. MR 97a:11176
    • (1995) Pacific J. Math. , vol.17 , pp. 455-467
    • Louboutin, S.1
  • 12
    • 84966247818 scopus 로고
    • Lower bounds for relative class numbers of CM-fields
    • Lou 5 MR 94d:11089
    • [Lou 5] S. Louboutin. Lower bounds for relative class numbers of CM-fields. Proc. Amer. Math. Soc. 120 (1994), 425-434. MR 94d:11089
    • (1994) Proc. Amer. Math. Soc. , vol.120 , pp. 425-434
    • Louboutin, S.1
  • 13
    • 33646903284 scopus 로고    scopus 로고
    • Majorations explicites du résidu au point 1 des fonctions zêta des corps de nombres, to appear in the
    • Lou 6
    • [Lou 6] S. Louboutin. Majorations explicites du résidu au point 1 des fonctions zêta des corps de nombres, to appear in the Journal of the Mathematical Society of Japan.
    • Journal of the Mathematical Society of Japan.
    • Louboutin, S.1
  • 14
    • 0012449494 scopus 로고    scopus 로고
    • Determination of all quaternion octic CM-fields with class number 2
    • Lou 7 CMP 96:17.
    • [Lou 7] S. Louboutin. Determination of all quaternion octic CM-fields with class number 2. J. London Math. Soc. (2) 54 (1996), 227-238. CMP 96:17.
    • (1996) J. London Math. Soc. , vol.2 , Issue.54 , pp. 227-238
    • Louboutin, S.1
  • 15
    • 0002151893 scopus 로고
    • Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
    • Lou-Oka MR 95g:11107
    • [Lou-Oka] S. Louboutin and R. Okazaki. Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one. Acta Arith. 67 (1994), 47-62. MR 95g:11107
    • (1994) Acta Arith. , vol.67 , pp. 47-62
    • Louboutin, S.1    Okazaki, R.2
  • 16
    • 0001870049 scopus 로고
    • Sur l'arithmétique des extensions galoisiennes à groupe de galois diédral d'ordre 2p
    • Mar MR 41:6820
    • [Mar] J. Martinet. Sur l'arithmétique des extensions galoisiennes à groupe de galois diédral d'ordre 2p. Ann. Inst. Fourier, Grenoble 19 (1969), 1-80. MR 41:6820
    • (1969) Ann. Inst. Fourier, Grenoble , vol.19 , pp. 1-80
    • Martinet, J.1
  • 17
    • 0001601336 scopus 로고
    • Notes on small class number
    • MW MR 50:9841
    • [MW] H.L. Montgomery and P.J. Weinberger. Notes on small class number. Acta Arith. 24 (1974), 529-542. MR 50:9841
    • (1974) Acta Arith. , vol.24 , pp. 529-542
    • Montgomery, H.L.1    Weinberger, P.J.2
  • 18
    • 0000123641 scopus 로고
    • Some analytic estimates of class numbers and discriminants
    • Odl MR 51:12788
    • [Odl] A.M. Odlyzko. Some analytic estimates of class numbers and discriminants. Inventiones Math. 29 (1975), 279-286. MR 51:12788
    • (1975) Inventiones Math. , vol.29 , pp. 279-286
    • Odlyzko, A.M.1
  • 19
    • 33646911400 scopus 로고    scopus 로고
    • Ol Table des corps cubiques réels de discriminant inférieur à 50000, avec base d'entiers, nombre de classes, régulateur et unités fondamentales. (January 1992), private communication.
    • [Ol] M. Olivier. Table des corps cubiques réels de discriminant inférieur à 50000, avec base d'entiers, nombre de classes, régulateur et unités fondamentales. (January 1992), private communication.
    • Olivier, M.1
  • 20
    • 84966218136 scopus 로고
    • The determination of all imaginary quartic abelian number fields with class number 1
    • Set MR 81k:12005
    • [Set] B. Setzer. The determination of all imaginary quartic abelian number fields with class number 1. Math. Comp. 35 (1980), 1383-1386. MR 81k:12005
    • (1980) Math. Comp. , vol.35 , pp. 1383-1386
    • Setzer, B.1
  • 21
    • 0001909901 scopus 로고
    • A complete determination of the complex quadratic fields of class-number one
    • Sta 1 MR 36:5102
    • [Sta 1] H.M. Stark. A complete determination of the complex quadratic fields of class-number one. Michigan Math. J. 14 (1967), 1-27. MR 36:5102
    • (1967) Michigan Math. J. , vol.14 , pp. 1-27
    • Stark, H.M.1
  • 22
    • 84966236823 scopus 로고
    • On complex quadratic fields with class-number two
    • Sta 2 MR 51:5548
    • [Sta 2] H.M. Stark. On complex quadratic fields with class-number two. Math. Comp. 29 (1975), 289-302. MR 51:5548
    • (1975) Math. Comp. , vol.29 , pp. 289-302
    • Stark, H.M.1
  • 23
    • 0001468947 scopus 로고
    • Some effective cases of the Brauer-Siegel theorem
    • Sta 3 MR 49:7218
    • [Sta 3] H.M. Stark. Some effective cases of the Brauer-Siegel theorem. Invent. Math. 23 (1974), 135-152. MR 49:7218
    • (1974) Invent. Math. , vol.23 , pp. 135-152
    • Stark, H.M.1
  • 24
    • 84967787224 scopus 로고
    • Class numbers of totally imaginary quadratic extensions of totally real fields
    • Sun MR 47:184
    • [Sun] J.S. Sunley. Class numbers of totally imaginary quadratic extensions of totally real fields. Trans. Amer. Math. Soc. 175 (1973), 209-232. MR 47:184
    • (1973) Trans. Amer. Math. Soc. , vol.175 , pp. 209-232
    • Sunley, J.S.1
  • 26
    • 84968482167 scopus 로고
    • The determination of the imaginary abelian number fields with class-number one
    • Yam MR 94g:11096
    • [Yam] K. Yamamura. The determination of the imaginary abelian number fields with class-number one. Math. Comp. 62 (1994), 899-921. MR 94g:11096
    • (1994) Math. Comp. , vol.62 , pp. 899-921
    • Yamamura, K.1


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