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By truncating the Fourier transform, Pólya managed to prove that the Xi function on the critical line was approximately

$$\xi(1/2+is) = (2\pi)^2 ( K_{9/4+is/2}( 2\pi) +K_{9/4-is/2}( 2\pi))$$

If this approximation is valid, why is it not considered that Pólya solved RH??

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oh thanks michael i did not know what mistake did i :) sorry – Jose Garcia Oct 20 '11 at 20:03
What is $K_y(x)$? – Qiaochu Yuan Oct 20 '11 at 22:53
What is happening here? Jose is responding to an invisible comment by michael? and the rest of us don't know what mistake was made, so we don't know what to make of the question? – Gerry Myerson Oct 21 '11 at 0:05
RH isn't something you "solve," it's something you prove, and finding an approximation does not strictly prove anything. – anon Oct 21 '11 at 0:07
@Qiaochu: it's the modified Bessel function of the second kind. – J. M. Oct 21 '11 at 1:35

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