Outdated Archival Version

These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.math.psu.edu/era/.

This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/

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

TeX source (21K)
DVI (29K)
PostScript (117K)

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.