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## Main Question or Discussion Point

Let be the series

[tex] \sum_{p<N}e^{2\pi p ix}=f(x) [/tex] where the sum is intended to be

over all primes less or equal than a given N.

My question is if there are approximate methods to evaluate this series for N big , since for a big prime the exponential sum is very oscillating would it be an 'intelligent' form to evaluate it for big N?, of course we know the trivial bound [tex] f(x)<\pi(N) [/tex] however i think this is rather useless.

[tex] \sum_{p<N}e^{2\pi p ix}=f(x) [/tex] where the sum is intended to be

over all primes less or equal than a given N.

My question is if there are approximate methods to evaluate this series for N big , since for a big prime the exponential sum is very oscillating would it be an 'intelligent' form to evaluate it for big N?, of course we know the trivial bound [tex] f(x)<\pi(N) [/tex] however i think this is rather useless.