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Results tagged with analytic-number-theory
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user 76335
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.
0
votes
Logarithmic integral, $π(x)$ and $x/(\ln x)$
Just to address the question $\pi(X) \geq \frac{X}{\log X}$? The above answers are sufficient -- let's just see why that is elementarily.
Let's assume RH just to illustrate the following idea/approxi …
- 138
7
votes
Accepted
Easiest way to see that $\zeta_{\mathbb{Z}[i]}(s) = \zeta(s) L(s, \chi)$?
As mentioned in the comment, the trick is to look in the Euler product (which holds in the half plane of $Re(s)$ large enough and then extend by analytic continuation). Since it's an arithmetic identi …
- 138