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Results tagged with asymptotics
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user 6043
Asymptotic behavior of functions, asymptotic series and related topics
9
votes
2
answers
4k
views
Product of Fibonacci numbers
Consider the counting function
$$
f(x)=|\{n\le x:n\text{ is a product of Fibonacci numbers}\}|
$$
so for example $f(4)=4=|\{1,2,3,4\}|$ since 1, 2, and 3 are Fibonacci numbers and $4=F_3\cdot F_3.$ (S …
- 9,114
29
votes
7
answers
7k
views
Asymptotic density of k-almost primes
Let $\pi_k(x)=|\{n\le x:n=p_1p_2\cdots p_k\}|$ be the counting function for the k-almost primes, generalizing $\pi(x)=\pi_1(x)$. A result of Landau is
$$\pi_k(x)\sim\frac{x(\log\log x)^{k-1}}{(k-1)!\l …
- 9,114
0
votes
2
answers
332
views
Error term in França-LeClair approximation of zeta zeros
The imaginary part of the $n$th critical zero of the Riemann zeta function with positive imaginary part (in increasing order) is asymptotically
$$
t_n \sim 2\pi\frac{n}{\log n}
$$
and has been approxi …
- 9,114