Sums of inverses in thin sets of finite fields
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- by Igor E. Shparlinski and Ana Zumalacárregui PDF
- Proc. Amer. Math. Soc. 146 (2018), 1377-1388 Request permission
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.References
Additional Information
- Igor E. Shparlinski
- Affiliation: Department of Pure Mathematics, University of New South Wales, 2052 NSW, Australia
- MR Author ID: 192194
- 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
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1377-1388
- MSC (2010): Primary 11B30, 11T30
- DOI: https://doi.org/10.1090/proc/13915
- MathSciNet review: 3754326