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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



The classical trilogarithm, algebraic $K$-theory of fields, and Dedekind zeta functions

Author: A. B. Goncharov
Journal: Bull. Amer. Math. Soc. 24 (1991), 155-162
MSC (1985): Primary 19F27, 11F67
MathSciNet review: 1056557
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  • [Bel] A. A. Beilinson, Polylogarithm and cyclotomic elements, preprint 1989.
  • A. Beĭlinson, Height pairing between algebraic cycles, Current trends in arithmetical algebraic geometry (Arcata, Calif., 1985), Contemp. Math., vol. 67, Amer. Math. Soc., Providence, RI, 1987, pp. 1–24. MR 902590, 10.1090/conm/067/902590
  • [B1 ] S. Bloch, Higher regulators, algebraic K-theory and zeta functions of elliptic curves, Lecture Notes, University of California, Irvine, 1977.
  • Armand Borel, Cohomologie de 𝑆𝐿_{𝑛} et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), no. 4, 613–636 (French). MR 0506168
  • Richard M. Hain and Robert MacPherson, Higher logarithms, Illinois J. Math. 34 (1990), no. 2, 392–475. MR 1046570
  • [K] E. E. Kummer, J. Pure Appl., (Crelle) 21 (1840).
  • Leonard Lewin, Polylogarithms and associated functions, North-Holland Publishing Co., New York-Amsterdam, 1981. With a foreword by A. J. Van der Poorten. MR 618278
  • S. Lichtenbaum, Values of zeta-functions at nonnegative integers, Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983) Lecture Notes in Math., vol. 1068, Springer, Berlin, 1984, pp. 127–138. MR 756089, 10.1007/BFb0099447
  • John Milnor, Introduction to algebraic 𝐾-theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. Annals of Mathematics Studies, No. 72. MR 0349811
  • John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. MR 0174052
  • Dinakar Ramakrishnan, Analogs of the Bloch-Wigner function for higher polylogarithms, Applications of algebraic 𝐾-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 371–376. MR 862642, 10.1090/conm/055.1/862642
  • [S] W. Spence, An essay on logarithmic transcendents, London and Edinburgh, 1809, pp. 26-34.
  • A. A. Suslin, Algebraic 𝐾-theory of fields, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 222–244. MR 934225
  • A. A. Suslin, Homology of 𝐺𝐿_{𝑛}, characteristic classes and Milnor 𝐾-theory, Algebraic 𝐾-theory, number theory, geometry and analysis (Bielefeld, 1982), Lecture Notes in Math., vol. 1046, Springer, Berlin, 1984, pp. 357–375. MR 750690, 10.1007/BFb0072031
  • Don Zagier, The Bloch-Wigner-Ramakrishnan polylogarithm function, Math. Ann. 286 (1990), no. 1-3, 613–624. MR 1032949, 10.1007/BF01453591
  • Don Zagier, Hyperbolic manifolds and special values of Dedekind zeta-functions, Invent. Math. 83 (1986), no. 2, 285–301. MR 818354, 10.1007/BF01388964
  • Don Zagier, Polylogarithms, Dedekind zeta functions and the algebraic 𝐾-theory of fields, Arithmetic algebraic geometry (Texel, 1989) Progr. Math., vol. 89, Birkhäuser Boston, Boston, MA, 1991, pp. 391–430. MR 1085270

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