New results on sum‐product type growth over fields
We prove a range of new sum‐product type growth estimates over a general field, in
particular the special case. They are unified by the theme of “breaking the threshold” …
particular the special case. They are unified by the theme of “breaking the threshold” …
[PDF][PDF] Distinct distances: open problems and current bounds
A Sheffer - arXiv preprint arXiv:1406.1949, 2014 - arxiv.org
arXiv:1406.1949v3 [math.CO] 2 Jul 2018 Page 1 arXiv:1406.1949v3 [math.CO] 2 Jul 2018
Distinct Distances: Open Problems and Current Bounds Adam Sheffer∗ Abstract We survey the …
Distinct Distances: Open Problems and Current Bounds Adam Sheffer∗ Abstract We survey the …
A sharp exponent on sum of distance sets over finite fields
We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More
precisely, let E and F be sets in F _q^ d F qd, and Δ (E), Δ (F) Δ (E), Δ (F) be corresponding …
precisely, let E and F be sets in F _q^ d F qd, and Δ (E), Δ (F) Δ (E), Δ (F) be corresponding …
Products of differences over arbitrary finite fields
B Murphy, G Petridis - arXiv preprint arXiv:1705.06581, 2017 - arxiv.org
There exists an absolute constant $\delta> 0$ such that for all $ q $ and all subsets $
A\subseteq\mathbb {F} _q $ of the finite field with $ q $ elements, if $| A|> q^{2/3-\delta} …
A\subseteq\mathbb {F} _q $ of the finite field with $ q $ elements, if $| A|> q^{2/3-\delta} …
A second wave of expanders in finite fields
B Murphy, G Petridis - Combinatorial and Additive Number Theory, New …, 2015 - Springer
This is an expository survey on recent sum-product results in finite fields. We present a
number of sum-product or “expander” results that say that if| A|> p^ 2/3, then some set …
number of sum-product or “expander” results that say that if| A|> p^ 2/3, then some set …
Incidences of Möbius Transformations in
A Warren, J Wheeler - Discrete & Computational Geometry, 2023 - Springer
We develop the methods used by Rudnev and Wheeler (2022) to prove an incidence
theorem between arbitrary sets of Möbius transformations and point sets in F p 2. We also …
theorem between arbitrary sets of Möbius transformations and point sets in F p 2. We also …
A new bound on Erd\H {o} s distinct distances problem in the plane over prime fields
In this paper we obtain a new lower bound on the Erd\H {o} s distinct distances problem in
the plane over prime fields. More precisely, we show that for any set $ A\subset\mathbb {F} …
the plane over prime fields. More precisely, we show that for any set $ A\subset\mathbb {F} …
Expanding phenomena over matrix rings
In this paper, we study expanding phenomena in the setting of matrix rings. More precisely,
we will prove that• if A is a set of M 2(𝔽 q) and| A|≫ q 7/2, then| A(A+ A)|,| A+ A A|≫ q …
we will prove that• if A is a set of M 2(𝔽 q) and| A|≫ q 7/2, then| A(A+ A)|,| A+ A A|≫ q …
Exponential sum estimates over prime fields
Exponential sum estimates over prime fields Page 1 International Journal of Number Theory
Vol. 16, No. 2 (2020) 291–308 c© World Scientific Publishing Company DOI: 10.1142/S1793042120500153 …
Vol. 16, No. 2 (2020) 291–308 c© World Scientific Publishing Company DOI: 10.1142/S1793042120500153 …
[HTML][HTML] Expanding phenomena over higher dimensional matrix rings
N Van The - Journal of Number Theory, 2020 - Elsevier
In this paper, we study the expanding phenomena in the setting of higher dimensional matrix
rings. More precisely, we obtain a sum-product estimate for large subsets and show that x …
rings. More precisely, we obtain a sum-product estimate for large subsets and show that x …