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Undergraduate Friday Seminar: Visualizing Number-Theoretic Fourier Series

Event Type
245 Altgeld Hall
Dec 3, 2021   4:00 pm  
Nick Kokkines and Andre Park (senior and freshman undgrads, UIUC Math)
Derek Thomas

We use Mathematica to explore Fourier series with coefficients given by number-theoretic functions, such as the Moebius function.  By plotting the trajectories of such Fourier series in the complex plane, we observe a remarkable variety of behaviors, ranging from fractal-like patterns to smooth curves to chaotic and unpredictable outcomes. In certain cases, we were able to explain the observed behavior, while in others, we formulated conjectures that predict the type of pattern that can arise.

Of course, there will be free pizza to-go courtesy of the IGL!

Hope to see you there!

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