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math.CO2026
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…
math.CA2026
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…
math.CO2026
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…