6 papers
A sharp point-sphere incidence bound for -Salem sets
Steven Senger, Dung The Tran
We establish a sharp point-sphere incidence bound in finite fields for point sets exhibiting controlled additive structure. Working in the framework of \((4,s)\)-Salem sets, which…
Parabolic distance in : a sharp exponent and new results
Dao Nguyen Van Anh, Steven Senger, Dung The Tran +1
We study the parabolic variant of the Erd\H os--Falconer distance problem in finite fields. That is, if is odd, we seek size thresholds beyond which any subset $E\subset \mathb…
On the number of 3APs in fractal sets
Marc Carnovale, Steven Senger
We use techniques from the study of the Falconer distance conjecture to explore conditions which guarantee largeness (in terms of bounded density/Lebesgue measure and Hausdor…
More on the number of distinct values of a class of functions
Robert Coulter, Steven Senger
In a previous article the authors determined the best-known upper bound for the cardinality of the image set for several classes of functions, including planar functions. Here, we…
Some observations on bent and planar functions
Robert S. Coulter, Steven Senger
We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a fu…
Triangular gaps in the most frequent sizes of for
Steven Senger
We explain the triangular gaps observed experimentally in the most popular sizes of the -fold iterated sumset, when is a randomly chosen four-element subset of the fir…