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Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

Published online by Cambridge University Press:  20 November 2018

Simon Macourt ,
Ilya D. Shkredov  and
Igor E. Shparlinski
Simon Macourt
Affiliation:
Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia, e-mail: s.macourt@unsw.edu.au
Ilya D. Shkredov
Affiliation:
Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, Russia, 119991, and Institute for Information Transmission Problems of Russian Academy of Sciences, Bolshoy Karetny Per. 19, Moscow, Russia, 127994, and MIPT, Institutskii per. 9, Dolgoprudnii, Russia, 141701, e-mail: ilya.shkredov@gmail.com
Igor E. Shparlinski
Affiliation:
Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia, e-mail: igor.shparlinski@unsw.edu.au
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Abstract

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We prove a new bound on collinear triples in subgroups of prime finite fields and use it to give some new bounds on exponential sums with trinomials.

Keywords

11L0711T23exponential sumsparse polynomialtrinomial
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 70 , Issue 6 , 01 December 2018 , pp. 1319 - 1338
Copyright
Copyright © Canadian Mathematical Society 2018

References

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