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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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Analytic continuation of a certain Euler product

What is known about analytic continuation of the following product ($\forall p:u_p\in\mathbb{C}$ with $|u_p |\leq 1$): $\prod\limits_{p\in\mathbb{P}} \left( 1-u_p p^{-s} \right)^{-1}$ Clearly, I a …
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