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Results tagged with analytic-number-theory
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user 3206
On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
2
votes
Accepted
Distribution of composite numbers
I would like to maintain my basic position on the other post: that this forum does not do well with questions that frequently change. Since the last version has hit rather close to home, I will remar …
- 3,209
2
votes
Distribution of composite numbers
I am afraid the weak version (at this writing) involving density being less than $1/(x-2)$ doesn't work either. Simply pick $d_i$ and $x$ near but less than $\sqrt{N}$, and
arrange $K$ and $L$ so tha …
- 3,209
2
votes
Smallest constant so that there are at least $n/\log_2{n}$ primes between $n$ and a constant...
Indeed, the suggestion given in the other thread is quite appropriate. Use a lower bound from Dusart for $\pi(cn)$, and an upper bound for $\pi(n)$, and you want the difference between these bounds t …
- 3,209
1
vote
Small quotients of smooth numbers
Here is some (unverified) computational data, which I encourage others to extend.
I look at the squarefree p-smooth numbers (being $2^k$ in number for $p$ being the $k$th
prime) and compared successi …
- 3,209
1
vote
Jacobsthal function related to squares
I take back what I said in the comments about the bound not shrinking. I am convinced that one can get much tighter bounds, and that the tighter bounds will depend massively on the quadratic residues …
- 3,209