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Results tagged with analytic-number-theory
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user 4672
A beautiful 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.
10
votes
3
answers
2k
views
What is the relationship between the Bell numbers, the Bell polynomials, and the partition n...
A friend of mine and I were wondering what relationship exists between the partition numbers $p_{n}$ and the Bell numbers $B_{n}$ (and also possibly the Bell polynomials $B_{n,k}(x_1,x_2,\dots,x_{n-k+ …
- 965
7
votes
3
answers
1k
views
What information do the roots of the generating function of the nontrivial zeroes of the Rie...
Let $a_{m}$ be the imaginary part of the nontrivial roots of the Riemann zeta function $\zeta(s)$. Suppose we have their generating function $u(x)=\sum_{m=1}^{\infty} a_{m}x^{m}=14.134725\ldots{}x^{1} …
- 965
11
votes
1
answer
467
views
turn $\pi/n$, move $1/n$ forward
start at the origin, first step number is 1.
turn $\pi/n$
move $1/n$ units forward
Angles are cumulative, so this procedure is equivalent (finitely)
to
$$
u(k):=\sum_{n=1}^{k} \frac{\exp(\pi i …
- 965