Asymptotic Euler-Maclaurin formula over lattice polytopes
Abstract
An asymptotic expansion formula of Riemann sums over lattice polytopes is given. The formula is an asymptotic form of the local Euler-Maclaurin formula due to Berline-Vergne. The proof given here for Delzant lattice polytopes is independent of the local Euler-Maclaurin formula. But we use it for general lattice polytopes. As corollaries, an explicit formula for each term in the expansion over Delzant polytopes in two dimension and an explicit formula for the third term of the expansion for Delzant polytopes in arbitrary dimension are given. Moreover, some uniqueness results are given.
Cite
@article{arxiv.0908.3073,
title = {Asymptotic Euler-Maclaurin formula over lattice polytopes},
author = {Tatsuya Tate},
journal= {arXiv preprint arXiv:0908.3073},
year = {2017}
}
Comments
35 pages. Results in the previous version are generalized to lattice polytopes. Some further results are added. The title is changed. The organization is changed to clarify the discussion.