Abstract
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 q0.5+ε, where ε is an arbitrarily small fixed number.
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Original Russian Text © M. A. Korolev, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 5, pp. 720–729.
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Korolev, M.A. Elementary Proof of an Estimate for Kloosterman Sums with Primes. Math Notes 103, 761–768 (2018). https://doi.org/10.1134/S0001434618050085
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DOI: https://doi.org/10.1134/S0001434618050085