# Evaluation of sums with the Möbius function $\mu (n)$

assuming RH true , for big 'x' how would the sums

$$\sum_{n=1}^{x} \mu (n) f(n)$$

as $x \to \infty$ ?

my guess, if all the zeros have real part $1/2$ then

$$\sum_{n=1}^{x} \mu (n) f(n)\sim \int_{1}^{x}\frac{dt}{\sqrt{x}}f(t)cos(at+b)$$

here 'a' and 'b' are real numbers

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