Timeline for An introduction to sieve method and their application, Cojocaru & Murty

8 events

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May 1, 2014 at 18:22	comment	added	rlo		Actually, wait. Unless I'm missing something, their claimed error term is wrong, and it should be $O(1/\log x)$ rather than $O(1/x^{1/4})$ (this is fine for their purposes, as the error on the next line is $O(1/\log x)$ anyway). To see it has to be at least this big, just look at the integral of the error from 3 to 4. To see that it's no bigger, split the integral into two parts, integrating from 3 to $x^{1/2}$, say, and from $x^{1/2}$ to $x$. The latter decays like $x^{-1/8}$, while the former can be bounded by $O(1/\log x)$.
May 1, 2014 at 17:32	comment	added	rlo		Plugging in the lemma, you'd get an $A_1 \log t$ term. This is the same as $-A_1(1+\log(x/t))+A_1\log x + A_1$. Is that your question?
May 1, 2014 at 8:29	history	edited	Doorbell	CC BY-SA 3.0	edited body
Apr 30, 2014 at 14:03	comment	added	Salvo Tringali		You should definitely replace the '$x$' appearing as an upper bound for the variable $\delta$ in the expression of the integral $I$ with '$t$'.
Apr 30, 2014 at 13:01	answer	added	Igor Rivin		timeline score: 1
Apr 30, 2014 at 8:58	history	edited	Doorbell	CC BY-SA 3.0	added 371 characters in body
Apr 30, 2014 at 8:39	review	First posts
Apr 30, 2014 at 8:59
Apr 30, 2014 at 8:24	history	asked	Doorbell	CC BY-SA 3.0