# Does the integral of squared Shah function exist?

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 $f^2$? –  Mose Wintner Apr 23 '11 at 15:26

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.