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 …

The first purpose of this paper is to provide new finite field extension theorems for
paraboloids and spheres. By using the unusual good Fourier transform of the zero sphere in …

For d⩾ 2 d\geqslant2 and an odd prime power qq, consider the vector space F qd F_q^d
over the finite field F q F_q, where the distance between two points (x 1,…, xd) (x_1,...,x_d) …

In this paper, we prove the first incidence bound for points and conics over prime fields. As
applications, we prove new results on expansion of bivariate polynomial images and on …

In this paper, we study the distribution of parallelograms and rhombi in a given set in the
plane over arbitrary finite fields F q 2. As an application, we improve the recent result due to …

In 2017, by using the group theoretic approach and tools from discrete Fourier analysis,
Bennett, Hart, Iosevich, Pakianathan, and Rudnev obtained a number of results on the …

On the additive energy of the distance set in finite fields - ScienceDirect Skip to main contentSkip
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Let $ A $ and $ B $ be sets in a finite vector space. In this paper, we study the magnitude of
the set $ A\cap f (B) $, where $ f $ runs through a set of transformations. More precisely, we …

The main purpose of this paper is to prove that the point-line incidence bound due to Vinh
(2011) over arbitrary finite fields can be improved in certain ranges by using tools from the …

For Borel subsets $\Theta\subset O (d)\times\mathbb {R}^ d $(the set of all rigid motions) and
$ E\subset\mathbb {R}^ d $, we define\begin {align*}\Theta (E):=\bigcup_ {(g …