- Volume 30 Issue 2
Todd series are associated to maximal non-degenerate lattice cones. The coefficients of Todd series of a particular class of lattice cones are closely related to generalized Dedekind sums of higher dimension. We generalize this construction and obtain an explicit formula for coefficients of the Todd series. It turns out that every maximal non-degenerate lattice cone, hence the associated Todd series can be obtained in this way.
Dedekind sum;lattice cone;Todd series
- M. Brion and M. Vergne, Lattice points in simple polytopes, J. Amer. Math. Soc. 10 (1997), no. 2, 371-392. https://doi.org/10.1090/S0894-0347-97-00229-4
- H. Chae, B. Jun, and J. Lee, An analogue of the Rademacher function for generalized Dedekind sums in higher dimension, Preprint.
- H. Chae, B. Jun, and J. Lee, Explicit reciprocity laws for generalized Dedekind sums and Todd coefficients, Preprint.
- F. Hirzebruch and D. Zagier, The Atiyah-Singer theorem and elementary number theory, Mathematics Lecture Series 3, Publish or Perish, Inc., Boston, MA, 1974.
- H. Rademacher and E. Grosswald, Dedekind Sums, Carus Math. Monogr. 16, The Mathematical Association of America, Washington, D.C., 1972.
- D. Zagier, Higher dimensional Dedekind sums, Math. Ann. 202 (1973), 149-172. https://doi.org/10.1007/BF01351173
Supported by : National Research Foundation of Korea(NRF)