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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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On the proof of Theorem 15.2 in Montgomery-Vaughan's Multiplicative number theory

I am trying to understand the proof of Theorem 15.2 in the aforementioned book. In this proof, the authors seem to infer that, if $\psi(x) - x < x^{\Theta - \epsilon}$ for every $\epsilon > 0$ and su …
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