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Let $f(x)=\sum_{s=-\infty}^{\infty}e^{-2\pi ixsk}$ $k$ integer. Does this integral exist? $\int_{0}^{1}(f(x))^{2}dx$

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    Have you tried proving continuity of $f^2$?2011-04-23

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I think the problem is, to have a meaning for $f(x)^2$, having in mind that the "Shah function" is merely a distribution (also known as Dirac comb). It is known that it is notoriously difficult to have a proper notion for the multiplication of distributions and I do not know a proper way of multiplying a $\delta$ with itself.