Geodesic
Elementary Proof of an Estimate for Kloosterman Sums with Primes
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 720-729

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A new elementary proof of an estimate for incomplete Kloosterman sums modulo a prime $q$ is obtained. Along with Bourgain's 2005 estimate of the double Kloosterman sum of a special form, it leads to an elementary derivation of an estimate for Kloosterman sums with primes for the case in which the length of the sum is of order $q^{0.5+\varepsilon}$, where $\varepsilon$ is an arbitrarily small fixed number.
Keywords: Kloosterman sum
Mots-clés : primes. 
@article{MZM_2018_103_5_a6,
     author = {M. A. Korolev},
     title = {Elementary {Proof} of an {Estimate} for {Kloosterman} {Sums} with {Primes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {720--729},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a6/}
}
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M. A. Korolev. Elementary Proof of an Estimate for Kloosterman Sums with Primes. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 720-729. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a6/