let be the exponential sum(adsbygoogle = window.adsbygoogle || []).push({});

[tex] S= \sum_{n=1}^{N}e( \frac{f(x)}{p}) [/tex]

[tex] e(x)= exp( 2i \pi x) [/tex]

my conjecture is that since the complex exponential takes its maximum value '1' when x is equal to an integer then

[tex] Re(S)= \Pi (f,N) [/tex] with [tex]\Pi (f,N) [/tex] is the number of solutions on the interval (1,N) of the congruence

[tex] f(x) =0 mod(p) [/tex] and f(x) is a Polynomial.

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# Exponential sums and congruences

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