Mathematische Annalen

, Volume 295, Issue 1, pp 1–24 | Cite as

Toric varieties, lattice points and Dedekind sums

  • James E. Pommersheim

Mathematics Subject Classification (1991)

14M25 11F20 52B20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Dan] Danilov, V.I.: The geometry of toric varieties. Russ. Math. Surv.33:2, 97–154 (1978)Google Scholar
  2. [Ehr] Ehrhart, E.: Sur un problème de géométrie diophantine linéaire. J. Reine Angew. Math.227, 1–29 (1967)Google Scholar
  3. [Ful] Fulton, W.: Intersection theory. Berlin Heidelberg New York: Springer 1984Google Scholar
  4. [Ham] Hammer, J.: Unsolved problems concerning lattice points. London San Francisco Melbourne: Pitman 1977Google Scholar
  5. [Hir] Hirzebruch, F.: Topological methods in algebraic geometry. Berlin Heidelberg New York: Springer 1966Google Scholar
  6. [HiZa] Hirzebruch, F., Zagier, D.: The Atiyah-Singer index theorem and elementary number theory. Berkeley: Publish or Perish 1974Google Scholar
  7. [Mo] Mordell, L.J.: Lattice points in a tetrahedron and generalized Dedekind sums. J. Indian Math.15, 41–46 (1951)Google Scholar
  8. [Mor] Morelli, R.: Pick's theorem and the Todd class of a toric variety (to appear)Google Scholar
  9. [My] Myerson, G.: On semi-regular continued fractions. Arch. Math.48, 420–425 (1987)Google Scholar
  10. [Oda] Oda, T.: Convex bodies and algebraic geometry. Berlin Heidelberg New York: Springer 1987Google Scholar
  11. [Ra] Rademacher, H.: Generalization of the reciprocity formula for Dedekind sums. Duke Math. J.21, 391–397 (1954)Google Scholar
  12. [RaGr] Rademacher, H., Grosswald, E.: Dedekind sums. (Carus Math. Monogr. no. 16) Washington: Mathematical Association of America 1972Google Scholar
  13. [Ree] Reeve, J.E.: On the volume of lattice polyhedra. Proc. Lond. Math. Soc., III. Ser.7, 378–395 (1957)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • James E. Pommersheim
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

Personalised recommendations