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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.

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Equidistribution of $\{\sqrt{p}: p \text{ primes }\}$ modulo 1

I am trying to show $\{\sqrt{p}: p \text{ primes }\}$ is equidistributed modulo 1. Using Weyl's criterion, it is sufficient to show for each nonzero integer $k$, \begin{equation} \sum_{n \leq x}e(k\s …
Kyle Yip's user avatar