Remote Access Bulletin of the American Mathematical Society

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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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,
  • [B1 ] S. Bloch, Higher regulators, algebraic K-theory and zeta functions of elliptic curves, Lecture Notes, University of California, Irvine, 1977.
  • [Bo] A. Borel, Cohomology de SL, Ann. Scuola Norm. Sup. Pisa C1. Sci. (4) 4, (1977), 613-636. MR 506168
  • 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,
  • [M] J. Milnor, Introduction to algebraic K-theory, Princeton, N.Y., 1971. MR 349811
  • [MM] J. Milnor and J. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264. MR 174052
  • 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,
  • [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,
  • Don Zagier, The Bloch-Wigner-Ramakrishnan polylogarithm function, Math. Ann. 286 (1990), no. 1-3, 613–624. MR 1032949,
  • Don Zagier, Hyperbolic manifolds and special values of Dedekind zeta-functions, Invent. Math. 83 (1986), no. 2, 285–301. MR 818354,
  • 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

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 19F27, 11F67

Retrieve articles in all journals with MSC (1985): 19F27, 11F67

Additional Information


American Mathematical Society