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CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS

Part of: Exponential sums and character sums Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  29 January 2019

Kui Liu ,
Igor E. Shparlinski  and
Tianping Zhang
Kui Liu
Affiliation:
School of Mathematics and Statistics, Qingdao University, No. 308, Ningxia Road, Shinan, Qingdao, Shandong 266071, P.R. China email liukui@qdu.edu.cn
Igor E. Shparlinski
Affiliation:
Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia email igor.shparlinski@unsw.edu.au
Tianping Zhang
Affiliation:
School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119 Shaanxi, P.R. China email tpzhang@snnu.edu.cn
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Abstract

We obtain a non-trivial bound for cancellations between the Kloosterman sums modulo a large prime power with a prime argument running over very short intervals, which in turn is based on a new estimate on bilinear sums of Kloosterman sums. These results are analogues of those obtained by various authors for Kloosterman sums modulo a prime. However, the underlying technique is different and allows us to obtain non-trivial results starting from much shorter ranges.

MSC classification

Primary: 11L05: Gauss and Kloosterman sums; generalizations 11T23: Exponential sums
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 475 - 487
Copyright
Copyright © University College London 2019 

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