An Euler-MacLaurin formula for polygonal sums

DOI10.1090/tran/8462zbMath1486.42007arXiv2004.09377OpenAlexW3159670423MaRDI QIDQ5020668

Leonardo Colzani, Giancarlo Travaglini, Luca Brandolini, Sinai Robins

Publication date: 7 January 2022

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09377

zbMATH Keywords

Fourier analysisdiscrepancyinteger pointsEuler-Maclaurin formulaapproximate quadratures

Mathematics Subject Classification ID

Approximate quadratures (41A55) Fourier series and coefficients in several variables (42B05) Euler-Maclaurin formula in numerical analysis (65B15) Irregularities of distribution, discrepancy (11K38)

Related Items (1)

Euler-Maclaurin summation formula on polytopes and expansions in multivariate Bernoulli polynomials

Cites Work

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• Euler-Maclaurin with remainder for a simple integral polytope
• Exact Euler-Maclaurin formulas for simple lattice polytopes
• Riemann sums over polytopes
• Sum-integral interpolators and the Euler-Maclaurin formula for polytopes
• CONCRETE POLYTOPES MAY NOT TILE THE SPACE
• Polygons Have Ears
• Local Asymptotic Euler-Maclaurin Expansion for Riemann Sums over a Semi-Rational Polyhedron
• Pick’s Theorem and Convergence of Multiple Fourier Series
• Computing the Continuous Discretely
• Convex and Discrete Geometry
• The Euler–Maclaurin formula for simple integral polytopes

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