Timeline for Is there an asymptotic formula that describes the correlation of multiplicative inverses in Farey sequences?
Current License: CC BY-SA 3.0
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| Apr 22, 2017 at 15:47 | history | bounty ended | CommunityBot | ||
| Apr 17, 2017 at 14:12 | history | edited | Max Alekseyev | CC BY-SA 3.0 |
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| Apr 17, 2017 at 14:11 | comment | added | Max Alekseyev | @KevinSmith: You are correct, there is no cancellation of the highest-order term under these bounds. I've removed the misleading statement from my answer. | |
| Apr 17, 2017 at 12:58 | comment | added | Kevin Smith | Thank you for your answer Max - this is a nice way to show that $\sum_{(a,q)=1}a a^*\sim Cq^2\varphi(q)$ for a constant $1/6\leq C\leq 1/3$. Perhaps I am missing something here but, even if $C=1/4$, this establishes only that $S(X)=o(X^{2})$ right? Of course one gets $O(X^{1+\epsilon})$ under the assumption of independence, but that is the reason behind expecting such cancellation (also that numerical data suggests the asymptotic is actually $\sim X/2$). | |
| Apr 17, 2017 at 12:32 | history | edited | Max Alekseyev | CC BY-SA 3.0 |
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| Apr 17, 2017 at 12:16 | history | edited | Max Alekseyev | CC BY-SA 3.0 |
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| Apr 17, 2017 at 12:07 | history | edited | Max Alekseyev | CC BY-SA 3.0 |
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| Apr 17, 2017 at 5:24 | history | answered | Max Alekseyev | CC BY-SA 3.0 |