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Feb
1
revised The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
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Feb
1
revised The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
added 79 characters in body
Feb
1
awarded  Revival
Feb
1
answered The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
Jan
19
awarded  Nice Answer
Jan
19
comment A possibly surprising appearance of Fibonacci numbers
@ClarkKimberling I've noticed that you've asked a lot of questions (24), but never accepted any answers. On the questions that you ask, for answer there is a small check mark underneath the up and down arrows for that answer. If someone answered one of your questions satisfactorily, you can click on the small check mark underneath the downarrow for that answer, and it will turn green. This marks the chosen answer as "accepted" and marks the question as having an accepted answer. It also rewards the user who answered your question.
Jan
19
revised When does this interesting sum diverge?
added 17 characters in body
Jan
19
answered When does this interesting sum diverge?
Jan
12
awarded  Yearling
Dec
10
comment The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
The short answer is that there will be no qualitative change to the error term in the prime number theorem. The best possible quantitative bounds for the mean value theorem can only change the constant in the Korobov-Vinogradov zero free region, that is the constant $c$ in $$\pi(x)=\text{li}(x)+O\left(x\exp\left(c\log(x)^{3/5}(\log \log x)^{-1/5}\right)\right).$$
Dec
4
comment Almost primes in short intervals
In the future, don't post identical questions on both MathOverflow and Math.Stackexchange within a 24 hour period. math.stackexchange.com/questions/1558632/… It is best to wait a couple of days to see if someone will answer on MSE before reposting it here.
Nov
10
comment On the mixed sum of three k-th powers
@StefanKohl: That heuristic is not accurate as $x,y$ and $z$ can take negative values. Other than using congruence's, it's not clear how to determine whether or not $n$ has infinitely many representations of the form $n=x^5+y^5+z^5$.
Nov
10
comment On the mixed sum of three k-th powers
Regarding zero density - can one even show that $x^{n}+y^{m}$ has zero density for any $n\neq m\geq 1$, not both even?
Nov
3
awarded  Nice Question
Oct
29
comment Subsets of [1..N] with no three-term arithmetic progressions and no large gaps
To be precise, and to eliminate trivial examples such as a set containing just a single point, we should include the wrap around gap. Say $l,s\in S$ are the largest and smallest elements in $S$ respectively, then include the gap $N-l+s$.
Oct
29
comment Subsets of [1..N] with no three-term arithmetic progressions and no large gaps
And you can't do better than this without improving Behrend's construction since if $g(N)$ is the upper bound for the size of the gap, then we have an arithmetic progression free set of size $\geq N/g(N)$
Oct
26
comment Square-free integers not divisible by any “small” primes
I believe that there is a factor of $k$ missing somewhere since $$\prod_{p\leq N^{1/k}}\left(1-\frac{1}{p}\right)\sim \frac{e^{-\gamma}}{\log N^{1/k}}=\frac{ke^{-\gamma}}{\log N}.$$
Oct
22
comment How big can a set of integers be if all pairs have small gcd?
@Lucia: You're right, I have edited the question for now, but I'll add in a nice form for the sum when $M>\sqrt{N}$
Oct
22
revised How big can a set of integers be if all pairs have small gcd?
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Oct
22
awarded  Enlightened