Computing the volume, counting integral points, and exponential sums

Computing the volume, counting integral points, and exponential sums. Barvinok, A. I. Discrete & Computational Geometry, 10(2):123–141, August, 1993.

Paper doi abstract bibtex

We design polynomial-time algorithms for some particular cases of the volume computation problem and the integral points counting problem for convex polytopes. The basic idea is a reduction to the computation of certain exponential sums and integrals. We give elementary proofs of some known identities between these sums and integrals and prove some new identities.

@article{barvinok_computing_1993,
	title = {Computing the volume, counting integral points, and exponential sums},
	volume = {10},
	issn = {1432-0444},
	url = {https://doi.org/10.1007/BF02573970},
	doi = {10.1007/BF02573970},
	abstract = {We design polynomial-time algorithms for some particular cases of the volume computation problem and the integral points counting problem for convex polytopes. The basic idea is a reduction to the computation of certain exponential sums and integrals. We give elementary proofs of some known identities between these sums and integrals and prove some new identities.},
	language = {en},
	number = {2},
	urldate = {2019-08-10},
	journal = {Discrete \& Computational Geometry},
	author = {Barvinok, Alexander I.},
	month = aug,
	year = {1993},
	keywords = {Arithmetic Operation, Exponential Integral, Integral Point, Poisson Summation Formula, Simple Cone},
	pages = {123--141}
}

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