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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.

4 votes

Partial sums of multiplicative functions

Here is a largely historical remark: Littlewood showed that there exists $x$ so that $\pi(x)$ is greater than the log-integral $\mathrm{li}(x)$. In fact, $\pi(x) - \mathrm{li}(x)$ is (more or less) …
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