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Elementary Proof of an Estimate for Kloosterman Sums with Primes

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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… Click to show full 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: proof estimate; kloosterman; estimate; elementary proof; kloosterman sums; estimate kloosterman

Journal Title: Mathematical Notes
Year Published: 2018

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