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edited Jun 22, 2022 at 8:13

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Caveat lector: as an answer to Timothy's question, this is tangential at best.

Regarding Gerry and Kevin's comments, people might be interested in Section 2 of these notes of mine these notes of mine from an undergraduate number theory course, in which the philosophy of "almost square root error" is batted around for a while, especially with regard to the Riemann hypothesis. This is maybe my favorite set of lecture notes from this course, perhaps because I got a chance to (talk and) write excitedly about things I hardly understand: I certainly do not claim a professional level of insight here. (Indeed some regulars on this site could do far better, and I would be interested to hear their critiques.)

The upshot though is that of agreement with Gerry and Kevin: having size $\sqrt{p}$ on the nose is just a little bit better than random, but the little bit makes a big difference: to me this suggests very precise structure rather than randomness.

Please see here for another take on the subject of almost square root error in the context of the Sato-Tate Conjecture. This latter article was written at almost the same time as mine, and the author happens to be my former thesis advisor. I am reasonably sure that both of these coincidences are indeed coincidental.

Caveat lector: as an answer to Timothy's question, this is tangential at best.

Regarding Gerry and Kevin's comments, people might be interested in Section 2 of these notes of mine from an undergraduate number theory course, in which the philosophy of "almost square root error" is batted around for a while, especially with regard to the Riemann hypothesis. This is maybe my favorite set of lecture notes from this course, perhaps because I got a chance to (talk and) write excitedly about things I hardly understand: I certainly do not claim a professional level of insight here. (Indeed some regulars on this site could do far better, and I would be interested to hear their critiques.)

The upshot though is that of agreement with Gerry and Kevin: having size $\sqrt{p}$ on the nose is just a little bit better than random, but the little bit makes a big difference: to me this suggests very precise structure rather than randomness.

Please see here for another take on the subject of almost square root error in the context of the Sato-Tate Conjecture. This latter article was written at almost the same time as mine, and the author happens to be my former thesis advisor. I am reasonably sure that both of these coincidences are indeed coincidental.

Caveat lector: as an answer to Timothy's question, this is tangential at best.

Regarding Gerry and Kevin's comments, people might be interested in Section 2 of these notes of mine from an undergraduate number theory course, in which the philosophy of "almost square root error" is batted around for a while, especially with regard to the Riemann hypothesis. This is maybe my favorite set of lecture notes from this course, perhaps because I got a chance to (talk and) write excitedly about things I hardly understand: I certainly do not claim a professional level of insight here. (Indeed some regulars on this site could do far better, and I would be interested to hear their critiques.)

The upshot though is that of agreement with Gerry and Kevin: having size $\sqrt{p}$ on the nose is just a little bit better than random, but the little bit makes a big difference: to me this suggests very precise structure rather than randomness.

Please see here for another take on the subject of almost square root error in the context of the Sato-Tate Conjecture. This latter article was written at almost the same time as mine, and the author happens to be my former thesis advisor. I am reasonably sure that both of these coincidences are indeed coincidental.

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created Jan 22, 2011 at 9:03

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Caveat lector: as an answer to Timothy's question, this is tangential at best.

Regarding Gerry and Kevin's comments, people might be interested in Section 2 of these notes of mine from an undergraduate number theory course, in which the philosophy of "almost square root error" is batted around for a while, especially with regard to the Riemann hypothesis. This is maybe my favorite set of lecture notes from this course, perhaps because I got a chance to (talk and) write excitedly about things I hardly understand: I certainly do not claim a professional level of insight here. (Indeed some regulars on this site could do far better, and I would be interested to hear their critiques.)

The upshot though is that of agreement with Gerry and Kevin: having size $\sqrt{p}$ on the nose is just a little bit better than random, but the little bit makes a big difference: to me this suggests very precise structure rather than randomness.

Please see here for another take on the subject of almost square root error in the context of the Sato-Tate Conjecture. This latter article was written at almost the same time as mine, and the author happens to be my former thesis advisor. I am reasonably sure that both of these coincidences are indeed coincidental.