The problem is concretely about Boolean functions of variables, and seems not to involve prime numbers at all. For any subset of the coordinate [indices], the corresponding Fourier coefficient is given by:
where is if is odd, and otherwise.
Note to Self. I need to play around with this concept a while.
Notation (from KLMMV • On the Fourier Spectrum of Symmetric Boolean Functions)
The order of a Fourier coefficient is
The Fourier expansion of is:
Added Notation (for shifting between coordinate indices and actual coordinates)
Begin with a survey of concrete examples, perhaps in tabular form.
For ease of reading formulas, let
To be continued …
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