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Results tagged with trigonometric-sums
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user 2024
4
votes
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Maximal minimum for a sum of two (or more) cosines
So we start with a rational $r=\frac{p}{q}$.
1) Say $2\not|p,2\not|q$. Then taking $x=q\pi$, we get:
$$f_r(x)=\cos(x)+\cos(rx)=\cos(q\pi)+\cos(p\pi)=-2$$
so $r$ is not the argmax.
2) Say $2$ divides …
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