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Results tagged with analytic-number-theory
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user 83999
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.
1
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0
answers
274
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Generalisation of the Liouville function as irreducible representations for the semigroup ($...
This is a duplicate of a question I have asked at here at math stack exchange, but I thought it could be also here of interest.
When looking at the [Liouville function] (https://en.wikipedia.org/wiki …
2
votes
1
answer
217
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Prime factor distribution over $\mathbb{N}$
I wonder if there is something like a general "prime component distribution pattern" of "the general natural number" $n$?
Using the following notation for the prime factorization $n = p_1^{\alpha_1}p_ …
1
vote
1
answer
192
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Asymptotics of cumulative Liouville function under RH versus simple random walk
The expectation values of the 1D simple random walk $S_n$ can be shown to have the asymptotic behavior of
$$ \lim_{n\to\infty} \frac{a_n}{n^{1/2}} = \sqrt{\frac{2}{\pi}}, \tag{1}\label{1}$$
with $a_n …