8 papers
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…
Peres--Schlag's nonempty-interior problem and a shifted-product variant for product sets
Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen
We study finite-field analogues of the Peres--Schlag nonempty-interior problem for product sets. Given \(A\subseteq\mathbb F_p\), we ask when a suitable one-dimensional linear imag…
On the Peres--Schlag orthogonal projection problem and Kakeya-type sets
Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen
We investigate the Peres--Schlag nonempty interior problem for orthogonal projections in both the finite-field and Euclidean settings. Over finite fields , we employ…
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…
A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin
Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou +1
This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Fursten…
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…
The Group Action Method and Radial Projection
Guo-Dong Hong, Chun-Yen Shen
The group action methods have been playing an important role in recent studies about the configuration problems inside a compact set in Euclidean spaces with given Hausdorff di…