Values of zeta functions at negative integers, Dedekind sums and toric geometry

Garoufalidis, Stavros¹ ; Pommersheim, James²

¹ School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
² Department of Mathematics, Pomona College, 610 North College Ave., Claremont, California 91711

Journal of the American Mathematical Society, Tome 14 (2001) no. 1, pp. 1-23

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-00-00352-0

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