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Results tagged with nt.number-theory
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user 83999
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
0
answers
2k
views
Recent progress on the verification of Mochizukis proof of the abc conjecture? [closed]
Apparently in preparation for the upcoming workshop on "Interuniversal Teichmüller Theory" in Kyoto in two weeks, which is intended to bring more light into Mochizukis proposed proof of the $abc$ conj …
2
votes
1
answer
217
views
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
views
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 …