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$$Z(t)= \sum_{n=1}^{\lfloor\sqrt t/2\pi\rfloor }\frac{\cos(N(t)-t\log p_{n})}{\sqrt n}$$

here $N(t)$ is the smooth part of the zeros and $ p_{n} $ are the primes since $ p_{n} =n\log n $ then $ \log p_{n}=\log n \log\log n $ for big $n$ so the convergence should be pretty similar

but is this approximaiton valid , here the sum over $n$ is made so $ p_{n} \le \lfloor\sqrt t/2\pi\rfloor$

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Did I correctly assume that "$int$" meant the integer part? –  martini Aug 8 '12 at 9:06
    
yes intx is integer part (or floor function) of 'x' i did not know how to put it –  Jose Garcia Aug 8 '12 at 9:22
    
You can write $\lfloor x \rfloor$ for $\lfloor x \rfloor$ –  martini Aug 8 '12 at 9:23
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