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Double Sums of Kloosterman Sums in Finite Fields
Simon Macourt, Igor E. Shparlinski
We bound double sums of Kloosterman sums over a finite field , with one or both parameters ranging over an affine space over its prime subfield ${\mathbb F}_p \sub…
Multilinear Exponential Sums With A General Class Of Weights
Bryce Kerr, Simon Macourt
In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered. Our techniques are base…
Decomposition of subsets in finite fields
Simon Macourt
We extend a bound of Roche-Newton, Shparlinski and Winterhof which says any subset of a finite field can be decomposed into two disjoint subset $\cU$ and $\cV$ of which the additiv…
Visible Points On Exponential Curves
Simon Macourt
We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible poi…
Incidence Results and Bounds of Trilinear and Quadrilinear Exponential Sums
Simon Macourt
We give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then u…
Bounds On Exponential Sums With Quadrinomials
Simon Macourt
We improve an existing result on exponential quadrilinear sums in the case of sums over multiplicative subgroups of a finite field and use it to give a new bound on exponential sum…