Euler-Maclaurin with remainder for a simple integral polytope

DOI10.1215/S0012-7094-05-13031-9zbMath1087.65002arXivmath/0307125OpenAlexW1966648998MaRDI QIDQ812551

Shlomo Sternberg, Jonathan Weitsman, Yael Karshon

Publication date: 24 January 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307125

zbMATH Keywords

polynomialsexponential functionslattice polytopesEuler-Maclaurin formulaconvex integral and regular polytopes

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Computational aspects related to convexity (52B55) Euler-Maclaurin formula in numerical analysis (65B15)

Related Items

Exact Euler-Maclaurin formulas for simple lattice polytopes, New polytope decompositions and Euler-Maclaurin formulas for simple integral polytopes, Asymptotic Euler-Maclaurin formula over lattice polytopes, Euler-Maclaurin summation formula on polytopes and expansions in multivariate Bernoulli polynomials, Polynomial behavior of special values of partial zeta functions of real quadratic fields at \(s = 0\), Local Asymptotic Euler-Maclaurin Expansion for Riemann Sums over a Semi-Rational Polyhedron, Spectral action for a one-parameter family of Dirac operators on $\bm{ SU}\textbf {(2)}$SU(2) and $\bm{SU}\textbf {(3)}$SU(3), Riemann sums over polytopes, Approximating sums by integrals only: multiple sums and sums over lattice polytopes, An Euler-MacLaurin formula for polygonal sums

Cites Work

• Geometric quantization and multiplicities of group representations
• A generalization of the Euler-Maclaurin formula
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• Toric varieties, lattice points and Dedekind sums
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• Riemann-Roch for toric orbifolds
• The Ehrhart polynomial of a lattice polytope
• The Frobenius problem, rational polytopes, and Fourier-Dedekind sums
• Theory of multi-fans
• Polytope Volume Computation
• THE GEOMETRY OF TORIC VARIETIES
• Genera of algebraic varieties and counting of lattice points
• Lattice points in simple polytopes
• The Euler–Maclaurin formula for simple integral polytopes
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