Fourier transform in cyclic groups
Abstract
On a cyclic group of prime order, the non-trivial Dirichlet characters together with their Fourier transforms have constant modulus outside 0 and vanish at 0. Answering a question of H. Cohn, we construct new functions with these properties. The proof relies on Floer homology. We also apply this method to the biunimodular functions problem.
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