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comment Estimating the integrated Tchebychev function and calculating its error
@AndrewKelley: thanks, will look at this.
Apr
4
revised Proving inequality $\frac{a}{\sqrt{a+2b}}+\frac{b}{\sqrt{b+2c}}+\frac{c}{\sqrt{c+2a}}\lt \sqrt{\frac{3}{2}}$
edited body
Apr
4
revised Proving inequality $\frac{a}{\sqrt{a+2b}}+\frac{b}{\sqrt{b+2c}}+\frac{c}{\sqrt{c+2a}}\lt \sqrt{\frac{3}{2}}$
added 385 characters in body
Apr
2
revised Proving inequality $\frac{a}{\sqrt{a+2b}}+\frac{b}{\sqrt{b+2c}}+\frac{c}{\sqrt{c+2a}}\lt \sqrt{\frac{3}{2}}$
added 132 characters in body
Mar
14
comment How much percentage are the Pythagorean triples among numbers?
Discussion of this point at p. 38 of Lehmer's paper.
Mar
14
revised How much percentage are the Pythagorean triples among numbers?
deleted 17 characters in body
Mar
9
accepted Elementary lemma about a rational sequence
Mar
9
revised Elementary lemma about a rational sequence
deleted 70 characters in body
Mar
9
asked Elementary lemma about a rational sequence
Mar
5
comment Bookkeeping question in claim about arithmetic functions in a proof
@MayankPandey: I haven't looked at this in 2 years but T(x) is defined in the first formula: a sum of $\psi$ functions. It occurs in Nagura's 1952 paper.
Jan
13
comment Origin of Littlewood's idea about sign changes of $Li(x) - \pi(x)$
Ingham, The Distr. of Prime Numbers, p. 92, note, cites Phragmen's result as a "less precise result pointing in the same direction" as that of Schmidt, who proved a Littlewood-type result but assumed the Riemann Hypothesis. Maybe this sharpens my question about your last paragraph (or not).
Jan
12
comment Origin of Littlewood's idea about sign changes of $Li(x) - \pi(x)$
I follow up to and agree with the "thin neighborhood" idea of your third-to-last paragraph. Phragmen's paper (1891) pre-dates Hadamard/de la Vallee Poussin's proofs of the prime number theorem (1896) so Phragmen didn't prove the existence of Chebyshev's limit. He proves that the difference $\pi(n)- Li(n)$ changes sign infinitely often, i.e. that $\pi(n)$ falls outside some neighborhood of $Li(n)$ infinitely often, which would seem to be a very different thing. Am I misunderstanding your last paragraph? Daniel Fischer's comments seemed correct to me...
Jan
7
awarded  Revival
Dec
1
comment Even numbers have more factors than odd numbers…
Abiding appreciation for this answer, especially given the badly expressed question. Thanks again.
Oct
24
awarded  Yearling
Oct
14
revised Regarding Chebyshev's theta function
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Oct
14
revised Regarding Chebyshev's theta function
added 89 characters in body
Oct
14
revised Regarding Chebyshev's theta function
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Oct
14
comment Proof of Hardy-Ramanujan inequality in number theory.
Maybe add a brief answer so this doesn't appear in the unanswered queue?
Oct
8
revised Regarding Chebyshev's theta function
added 534 characters in body