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Fix $y$ a positive real number. Is there an effective bound for the following sum i.e a positive constant B such that $$\sum_{p>y}\sum_{\nu \geq 4} \frac{1}{p^{9\nu/32}} \leq B.$$ Many thanks.

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Note that only considering the $\nu = 2$ terms gives $\frac{1}{p^{9/16}} > \frac{1}{p}$, and the sum of reciprocals of the primes diverges, so your sum is unbounded.

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