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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Values of zeta functions at negative integers, Dedekind sums and toric geometry
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by Stavros Garoufalidis and James E. Pommersheim PDF
J. Amer. Math. Soc. 14 (2001), 1-23 Request permission


We study relations among special values of zeta functions, invariants of toric varieties, and generalized Dedekind sums. In particular, we use invariants arising in the Todd class of a toric variety to give a new explicit formula for the values of the zeta function of a real quadratic field at nonpositive integers. We also express these invariants in terms of the generalized Dedekind sums studied previously by several authors. The paper includes conceptual proofs of these relations and explicit computations of the various zeta values and Dedekind sums involved.
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Additional Information
  • Stavros Garoufalidis
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
  • Email:
  • James E. Pommersheim
  • Affiliation: Department of Mathematics, Pomona College, 610 North College Ave., Claremont, California 91711
  • Email:
  • Received by editor(s): June 1, 1999
  • Received by editor(s) in revised form: May 24, 2000
  • Published electronically: September 18, 2000
  • Additional Notes: The authors were partially supported by NSF grants DMS-95-05105 and DMS-95-08972, respectively.

  • Dedicated: Dedicated to our teacher, W. Fulton
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 1-23
  • MSC (1991): Primary 11M06; Secondary 14M25, 11F20
  • DOI:
  • MathSciNet review: 1800347