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The Ehrhart Polynomial of a Lattice n-Simplex
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## The Ehrhart polynomial of a lattice n-simplex

### Ricardo Diaz and Sinai Robins

**Abstract.**
The problem of counting the number of lattice points inside a lattice
polytope in $\Bbb R^n$ has been studied from a variety of perspectives,
including the recent work of Pommersheim and Kantor-Khovanskii using
toric varieties and Cappell-Shaneson using Grothendieck-Riemann-Roch.
Here we show that the Ehrhart polynomial of a lattice $n$-simplex has
a simple analytical interpretation from the perspective of Fourier
Analysis on the $n$-torus. We obtain closed forms in terms of
cotangent expansions for the coefficients of the Ehrhart polynomial,
that shed additional light on previous descriptions of the Ehrhart
Polynomial.

*Copyright American Mathematical Society 1996*

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#### Article Info

- ERA Amer. Math. Soc.
**02** (1996), pp. 1-6
- Publisher Identifier: S 1079-6762(96)00001-7
- 1991
*Mathematics Subject Classification* Primary 52B20, 52C07, 14D25, 42B10, 11P21, 11F20, 05A15; Secondary 14M25, 11H06.
- Received by the editors August 4, 1995, and, in revised form, December 1,
1995
- Communicated by Svetlana Katok
- Comments (When Available)

**Ricardo Diaz **

Department of Mathematics,
University of Northen Colorado,
Greeley, Colorado 80639

*E-mail address:* `rdiaz@benthley.univnorthco.edu `

**Sinai Robins**

Department of Mathematics,
UVSD 9500 Gilman Drive,
La Jolla, CA 92093-0112

*E-mail address:* `srobins@ucsd.edu `

Research partially supported by NSF Grant #9508965.

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