i,m working on a method to obtain the Fourier series of the prime number counting function in the form :(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\pi(x)=\sum_{n=-\infty}^{\infty}c_{n}e^{in\pi{x}/L} [/tex]

the question is..would be this series useful?....we know that the prime number counting function is always an integer, so we only would need to know the function pi through the series with an error of 0.1 or 0.01 (so we shouln,t not take infinite terms), also with the aid of the series we could locate primes (as at x=p prime) the series exhibit Gib,s Phenomenon, also we could give asymptotic expressions for the sums:

[tex]\sum_{p}^f(x) [/tex] sum over all the primes p<L with L big.

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# Fourier complex series for Pi(x)

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