| DATE: | Thursday, March 14, 2002 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Sinai Robins, Temple University |
| TITLE: | A new class of zeta functions attached to cones and polytopes |
There is a fascinating connection between polyhedra and zeta functions defined over them. These new zeta functions are extensions of the Riemann zeta function, to several variables. The functions we study are similar to Shintani's zeta functions but in fact possess functional equations between the (simplicial) cone they are defined over, and its dual cone. Shintani's zeta functions do not possess functional equations. From the perspective of combinatorial geometry, these functions help enumerate weighted lattice points in objects, and from the perspective of number theory these functions are meromorphic extensions of the Riemann zeta function.