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Sums of inverses in thin sets of finite fields


Authors: Igor E. Shparlinski and Ana Zumalacárregui
Journal: Proc. Amer. Math. Soc. 146 (2018), 1377-1388
MSC (2010): Primary 11B30, 11T30
DOI: https://doi.org/10.1090/proc/13915
Published electronically: December 28, 2017
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Abstract: We obtain lower bounds for the cardinality of $ k$-fold sum-sets of reciprocals of elements of suitable defined short intervals in high degree extensions of finite fields. Combining our results with bounds for multilinear character sums we obtain new results on incomplete multilinear Kloosterman sums in finite fields.


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Additional Information

Igor E. Shparlinski
Affiliation: Department of Pure Mathematics, University of New South Wales 2052 NSW, Australia
Email: igor.shparlinski@unsw.edu.au

Ana Zumalacárregui
Affiliation: Department of Pure Mathematics, University of New South Wales 2052 NSW, Australia
Email: ana.zumalacarregui@gmail.com

DOI: https://doi.org/10.1090/proc/13915
Keywords: Finite fields, polynomials, inversions, sum-sets
Received by editor(s): December 6, 2016
Published electronically: December 28, 2017
Additional Notes: This work was supported by ARC Grant DP140100118
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society

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