Electronic Research Announcements

Author(s): Ricardo Diaz; Sinai Robins
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 1-6.
MSC (1991): Primary 52B20, 52C07, 14D25, 42B10, 11P21, 11F20, 05A15; Secondary 14M25, 11H06
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Abstract: The problem of counting the number of lattice points inside a lattice polytope in $\mathbb {R}^{n}$ 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.

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Ricardo Diaz
Affiliation: Department of Mathematics, University of Northern Colorado, Greeley, Colorado 80639
Email: rdiaz@bentley.univnorthco.edu

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