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math.NT2025
Generalised Fermat equations in dense variables over finite fields and rings
Sam Chow, Zi Li Lim, Akshat Mudgal
Let be a sufficiently dense subset of a finite field or a finite, cyclic ring . Assuming that and have no small prime divisors, we…
math.NT2025
On the density version of quadratic Waring's problem and the quadratic Waring--Goldbach problem
Zi Li Lim
We prove a sharp density theorem for quadratic Waring's problem over cyclic groups, when the number of variables is at least . Also, we obtain some new improvements on the densi…
math.NT2025
Uniform nonlinear Szemerédi theorem for corners in finite fields
Zi Li Lim
Let be rational functions such that and the constant function are linearly independent over , we prove an asymptotic formul…