In this section we will analyze the Fourier coefficients of $\mathrm{Maj}_n$. In fact, we give an explicit formula for them in Theorem 16 below. But most of the time this formula is not too useful; instead, it’s better to understand the Fourier coefficients of $\mathrm{Maj}_n$ asymptotically as $n \to \infty$.

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## Recent comments

Ohad Klein: Are the indexing in (the start of) 7 OK?Ohad Klein: "learning algorithm running in time in time"Amir: In the proof of Theorem 16, and in the equation immediately ...Ohad Klein: In example 6, should "of codimension less than n" be "of pos...Ohad Klein: In 15c (18c in the book), I think it should be $\cap_j{V_j}$...Ohad Klein: Bracket typo: In the proof of thm 10 (12 in the book), $sgn(...Ohad Klein: Oops, my bad.