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Let $\eta:[0,\infty)\to [0,\infty)$ satisfy $\eta(0)=1$ and $\int_0^\infty \eta(x) dx = 1$ (say). Write $M\eta$ for the Mellin transform of $\eta$. Let $\epsilon>0$ be small. What is the choice of $...

I am an undergraduate student writing an expository thesis on the complex-analytic proof of the Prime Number Theorem. I understand that applying the Mellin Transform to the partial sum of the van ...