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Bounds of Trilinear and Quadrilinear Exponential Sums

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Abstract

We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number of solutions of certain equations involving products and differences of sets in prime finite fields to give an explicit upper bound on trilinear exponential sums which improves the previous bound of Bourgain and Garaev (2009). We also obtain explicit bounds for quadrilinear exponential sums.

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Acknowledgements

The authors would like to thank Moubariz Garaev and Misha Rudnev for their comments and suggestions. The authors are also very grateful to the referee for the careful reading of the manuscript and valuable comments.

During the preparation of this paper, the first author was supported by the NSF DMS Grant 1500984, and the second author was supported by ARC Grant DP170100786.

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30602, USA

    Giorgis Petridis

  2. Department of Pure Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia

    Igor E. Shparlinski

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  1. Giorgis Petridis
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  2. Igor E. Shparlinski
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Correspondence to Igor E. Shparlinski.

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Petridis, G., Shparlinski, I.E. Bounds of Trilinear and Quadrilinear Exponential Sums. JAMA 138, 613–641 (2019). https://doi.org/10.1007/s11854-019-0028-4

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  • DOI: https://doi.org/10.1007/s11854-019-0028-4

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