On the Fourier Spectrum of MOD Functions

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Friday, 13 October 2017,
17:15 to 18:15

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We use exponential sums to analyze the Fourier spectrum of functions of the type MOD_m^A (with output in {-1, 1}), for any constant m, and a general accepting set A.  We will then see how this yields lower bounds on the number of monomials required by any real polynomial which sign represents MOD_m^A on all inputs.

No Fourier analysis background will be assumed, and I will start with a quick recap of the necessary Fourier analytic prerequisites.