# Effective estimates of exponential sums over primes

@inproceedings{Daboussi1996EffectiveEO, title={Effective estimates of exponential sums over primes}, author={Hedi Daboussi}, year={1996} }

- Published 1996
DOI:10.1007/978-1-4612-4086-0_13

The asymptotic behavior of the sum
$$S(x,\alpha ) = \sum\limits_{n \leqslant x} {\pi (n)e(n\alpha ),}$$
where α is real, e(α) = e2πiα, and Λ is the von Mangoldt function, has been extensively studied by many authors. It plays a central role in Vinogradov’s solution of the 3-primes conjecture [10]. It is also a main tool in the study of the equidistribution of the sequence {pα, p prime} modulo 1.

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## Minor arcs for Goldbach's problem

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## Explicit upper bounds for exponential sums over primes

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