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Mathematical Notes

, Volume 103, Issue 5–6, pp 761–768 | Cite as

Elementary Proof of an Estimate for Kloosterman Sums with Primes

  • M. A. Korolev
Article
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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.

Keywords

Kloosterman sum primes 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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