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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 :) sorry2011-10-20
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    What is $K_y(x)$?2011-10-20
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    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?2011-10-21
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    RH isn't something you "solve," it's something you **prove**, and finding an approximation does not strictly *prove* anything.2011-10-21
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    @Qiaochu: it's the modified Bessel function of the second kind.2011-10-21
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    however if polya equation is exact or approximate then it means that RH is true, anyway Odzlyzko and other evaluated the zeros using numerical approximations too2011-10-21
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    @Gerry, what happened is that Michael Hardy (silently) corrected some typos in the post. You may see the successive versions of a post by clicking on the link on the right of the mention *edited* which is on the left of the name of the asker at the bottom of the post.2011-10-22

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