Pick’s Theorem and Convergence of Multiple Fourier Series

DOI10.1080/00029890.2021.1839241zbMath1462.42015OpenAlexW3124808072MaRDI QIDQ5144495

Giancarlo Travaglini, Luca Brandolini, Leonardo Colzani, Sinai Robins

Publication date: 18 January 2021

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2021.1839241

zbMATH Keywords

Pick's theoremconvergence of multiple Fourier series

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Fourier series and coefficients in several variables (42B05)

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CONCRETE POLYTOPES MAY NOT TILE THE SPACE ⋮ An Euler-MacLaurin formula for polygonal sums

Cites Work

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• Integer points in polyhedra
• The Ehrhart polynomial of a lattice polytope
• Translational tilings by a polytope, with multiplicity
• CONCRETE POLYTOPES MAY NOT TILE THE SPACE
• From Euler's Formula to Pick's Formula Using an Edge Theorem
• Pick's Formula via the Weierstrass ℘-Function
• Computing the Continuous Discretely
• Pick's Theorem via Minkowski's Theorem

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