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Pick's theorem and Riemann sums: a Fourier analytic tale

By Giancarlo Travaglini

Appears in collection : Jean-Morlet Chair 2020 - Workshop: Discrepancy Theory and Applications - Part 1 / Chaire Jean-Morlet 2020 - Workshop : Théorie de la discrépance et applications - Part 1

We show a connection between Fourier series and a celebrated theorem of G. Pick on the number of integer points in an integer polygon. Then we discuss an Euler-Maclaurin formula over polygons.

Information about the video



  • BECK, Matthias et ROBINS, Sinai. Computing the continuous discretely. second edition Berlin : Springer science+ Business media, LLC, 2015. - http://dx.doi.org/10.1007/978-1-4939-2969-6
  • STEIN, E. M. et WEISS, G. Introduction to Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, 1971). Princeton Mathematical Series, no 32. -

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