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Divisibility of orders of K2 groups associated to quadratic fields

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EN
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EN
We discuss some divisibility results of orders of K-groups and cohomology groups associated to quadratic fields.
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Strony
277--284
Opis fizyczny
Bibliogr. 22 poz.
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Bibliografia
  • [1] J. Browkin, On the divisibility by 3 of #K2OF for real quadratic fields F, Demonstratio Math. 18(1) (1985), 153–159.
  • [2] J. Browkin, On the p-rank of the tame kernel of algebraic number fields, J. Reine Angew. Math. 432 (1992), 135–149.
  • [3] J. Browkin, Tame kernels of quadratic number fields: numerical heuristics, Funct. Approx. Comment. Math. 28 (2000), 35–43. Dedicated to Włodzimierz Staś on the occasion of his 75th birthday.
  • [4] D. Byeon, Indivisibility of special values of Dedekind zeta functions of real quadratic fields, Acta Arith. 109(3) (2003), 231–235.
  • [5] D. Byeon and E. Koh, Real quadratic fields with class number divisible by 3, Manu-scripta Math. 111(2) (2003), 261–263.
  • [6] H. Cohen and H. W. Lenstra, Jr. Heuristics on class groups of number fields, In Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), pages 33–62. Springer, Berlin, 1984.
  • [7] H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217(3) (1975), 271–285.
  • [8] I. Kimura, Some implications of indivisibility of special values of zeta functions of real quadratic fields, Math. J. Toyama Univ. 26 (2003), 85–91.
  • [9] M. Kolster, Higher relative class number formulae, Math. Ann. 323(4) (2002), 667–692.
  • [10] M. Kurihara, Some remarks on conjectures about cyclotomic fields and K-groups of Z, Compositio Math. 81(2) (1992), 223–236.
  • [11] Hong Wen Lu, Congruences for the class number of quadratic fields, Abh. Math. Sem. Univ. Hamburg 52 (1982), 254–258.
  • [12] B. Mazur and A. Wiles, Class fields of abelian extensions of Q, Invent. Math. 76(2) (1984), 179–330.
  • [13] C. Queen, A note on class numbers of imaginary quadratic number fields, Arch. Math. (Basel) 27(3) (1976), 295–298.
  • [14] J. Rognes, K4(Z) is the trivial group, Topology 39(2) (2000), 267–281.
  • [15] J.-P. Serre, Cohomologie des groupes discrets, In Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970), pages 77–169. Ann. of Math. Studies, No. 70. Princeton Univ. Press, Princeton, N.J., 1971.
  • [16] C. Soule, On the 3-torsion in K4(Z), Topology 39(2) (2000), 259–265.
  • [17] K. Soundararajan, Divisibility of class numbers of imaginary quadratic fields, J. London Math. Soc. (2) 61(3) (2000), 681–690.
  • [18] J. Urbanowicz, On the divisibility of generalized Bernoulli numbers, In Applications of algebraic K-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), volume 55 of Contemp. Math., pages 711–728. Amer. Math. Soc., Providence, RI, 1986.
  • [19] L. C. Washington, Introduction to Cyclotomic Fields, Springer-Verlag, New York, second edition, 1997.
  • [20] A. Wiles, The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131(3) (1990), 493–540.
  • [21] Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math. 7 (1970), 57–76.
  • [22] G. Yu, A note on the divisibility of class numbers of real quadratic fields, J. Number Theory 97(1) (2002), 35–44.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0022-0004
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