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Results tagged with analytic-number-theory
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user 17218
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.
4
votes
Dirichlet series of the reciprocal radical function
A complete answer is at Asymptotic behavior of a "strange" arithmetic function. The sum $\sum_{n \leq x} a_n$ is not $O(x (\log x)^A)$ for any $A$, due to the precise asymptotics stated there for the …
- 4,985
6
votes
Accepted
Asymptotics on sum of n/rad(n)
One has
\begin{align*}
\sum_{n \leq x}\frac{n}{\operatorname{rad}n} & = (1+o(1)) \, x \sqrt{\frac{2}{\log x \log \log x}} \exp\left((1+o(1))\sqrt{\frac{8\log x}{\log \log x}}\right) \ (x \to \infty), …
- 4,985
1
vote
Approximation for the $n$th nontrivial zero of $\zeta(s)$
I think I might now have an answer to my question, in that the approximation I gave should be within $O(1)$ of $t_n$, and it can be related to the function $N(T)$. However, I am not yet sure in what …
- 4,985
-1
votes
Accepted
Riemann–Von Mangoldt formula
Not sure why my answer received negative votes. I think it's correct. Someone please point out my errors?
EDITED TO REFLECT @LUCIA'S COMMENTS: After digging through a bunch of references, I sorted ou …
- 4,985
6
votes
Accepted
Primes which are safe and Sophie Germain
This is asking for the density of Cunningham chains of the first kind of length three. Take the integer polynomials $f_1(n) = n$, $f_2(n) = 2n+1$ and $f_3(n) = f_2(f_2(n)) = 4n+3$ and apply the (rema …
- 4,985