Riemann sums over polytopes

DOI10.5802/aif.2330zbMath1143.52011arXivmath/0608171OpenAlexW1925289970MaRDI QIDQ2477557

Victor W. Guillemin, Shlomo Sternberg

Publication date: 14 March 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0608171

zbMATH Keywords

Riemann sumsEhrhart's theoremEuler-Maclaurin formula for polytopes

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25)

Related Items

The equivariant Riemann-Roch theorem and the graded Todd class, Extremal Kähler Poincaré type metrics on toric varieties, Asymptotic Euler-Maclaurin formula over lattice polytopes, Euler-Maclaurin summation formula on polytopes and expansions in multivariate Bernoulli polynomials, Euler-Maclaurin formulas via differential operators, Local Asymptotic Euler-Maclaurin Expansion for Riemann Sums over a Semi-Rational Polyhedron, Semi-classical analysis of piecewise quasi-polynomial functions and applications to geometric quantization, Toric partial density functions and stability of toric varieties, Stability functions, The Mellin transform and spectral properties of toric varieties, Bergman metrics and geodesics in the space of Kähler metrics on principally polarized abelian varieties, Approximating sums by integrals only: multiple sums and sums over lattice polytopes, An Euler-MacLaurin formula for polygonal sums, Filtrations and test-configurations

Cites Work

• Euler-Maclaurin with remainder for a simple integral polytope
• Riemann-Roch for toric orbifolds
• THE GEOMETRY OF TORIC VARIETIES
• Lattice points in simple polytopes
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