[图书][B] Fourier analysis and Hausdorff dimension
P Mattila - 2015 - books.google.com
During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …
theory and Fourier analysis. This book describes part of that development, concentrating on …
Group actions and geometric combinatorics in
In this paper we apply a group action approach to the study of Erdős–Falconer-type
problems in vector spaces over finite fields and use it to obtain non-trivial exponents for the …
problems in vector spaces over finite fields and use it to obtain non-trivial exponents for the …
On the energy variant of the sum-product conjecture
We prove new exponents for the energy version of the Erdős–Szemerédi sum-product
conjecture, raised by Balog and Wooley. They match the previously established milestone …
conjecture, raised by Balog and Wooley. They match the previously established milestone …
On the pinned distances problem in positive characteristic
We study the Erdős–Falconer distance problem for a set A⊂ F 2 A⊂F^2, where FF is a field
of positive characteristic p p. If F= F p F=F_p and the cardinality| A| |A| exceeds p 5/4 p^5/4 …
of positive characteristic p p. If F= F p F=F_p and the cardinality| A| |A| exceeds p 5/4 p^5/4 …
Cycles of Arbitrary Length in Distance Graphs on
A Iosevich, G Jardine, B McDonald - Proceedings of the Steklov Institute of …, 2021 - Springer
Abstract For E ⊂\mathbb F_q^ d, d ≥ 2, where\mathbb F_q is the finite field with q elements,
we consider the distance graph\mathcal G^ dist _t (E), t ≠ 0, where the vertices are the …
we consider the distance graph\mathcal G^ dist _t (E), t ≠ 0, where the vertices are the …
On distinct perpendicular bisectors and pinned distances in finite fields
Given a set of points P⊂ F q 2 such that| P|≥ q 4/3, we establish that for a positive
proportion of points a∈ P, we have|{‖ a− b‖: b∈ P}|≫ q, where‖ a− b‖ is the distance …
proportion of points a∈ P, we have|{‖ a− b‖: b∈ P}|≫ q, where‖ a− b‖ is the distance …
Radial projection theorems in finite spaces
Motivated by recent results on radial projections and applications to the celebrated Falconer
distance problem, we study radial projections in the setting of finite fields. More precisely, we …
distance problem, we study radial projections in the setting of finite fields. More precisely, we …
Three-point configurations determined by subsets of via the Elekes-Sharir Paradigm
M Bennett, A Iosevich, J Pakianathan - Combinatorica, 2014 - Springer
We prove that if E ⊂ F _Q^ 2, q≡ 3 mod 4, has size greater than Cq^ 7 4, then E determines
a positive proportion of all congruence classes of triangles in F _q^ 2. The approach in this …
a positive proportion of all congruence classes of triangles in F _q^ 2. The approach in this …
Long paths in the distance graph over large subsets of vector spaces over finite fields
M Bennett, J Chapman, D Covert, D Hart… - arXiv preprint arXiv …, 2014 - arxiv.org
Let $ E\subset {\Bbb F} _q^ d $, the $ d $-dimensional vector space over a finite field with $ q
$ elements. Construct a graph, called the distance graph of $ E $, by letting the vertices be …
$ elements. Construct a graph, called the distance graph of $ E $, by letting the vertices be …
The quotient set of the quadratic distance set over finite fields
Let 𝔽 qd be the d-dimensional vector space over the finite field 𝔽 q with q elements. For
each non-zero r in 𝔽 q and E⊂ 𝔽 qd, we define W(r) as the number of quadruples (x, y, z …
each non-zero r in 𝔽 q and E⊂ 𝔽 qd, we define W(r) as the number of quadruples (x, y, z …