Bounds of Trilinear and Quadrilinear Exponential Sums

Bounds of Trilinear and Quadrilinear Exponential Sums

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 Gar...

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Veröffentlicht in:Journal d'analyse mathématique (Jerusalem) 2019-07, Vol.138 (2), p.613-641
Hauptverfasser: Petridis, Giorgis, Shparlinski, Igor E.
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Analysis
Dynamical Systems and Ergodic Theory
Fields (mathematics)
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
Sums
Upper bounds
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Zusammenfassung: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.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-019-0028-4