4 papers · 1 filter
Simultaneous popular polynomial differences in higher dimensions
Guo-Dong Hong
We extend the simultaneous popular polynomial difference theorem of Conlon, Dong, and the author to polynomial shifts along prescribed directions in . Let $P_1,\ldo…
Simultaneous popular polynomial differences over finite fields
David Conlon, Dingding Dong, Guo-Dong Hong
Green's popular difference theorem says that for every \(\varepsilon>0\), all sufficiently large primes \(p\), and every set \(A\subseteq\mathbb F_p\) of density \(α\), there exist…
On weighted multilinear polynomial averages in finite fields
Guo-Dong Hong
We study the weighted multilinear polynomial averages in finite fields. The essential ingredient is the -norm control of the corresponding weighted multilinear polynomial aver…
Three term rational function progressions in finite fields
Guo-Dong Hong, Zi Li Lim
Let be rational functions such that and the constant function are linearly independent over , we prove an asymptotic formul…