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

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Pick's theorem and Riemann sums: a Fourier analytic tale
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12
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CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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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.
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