We use an estimate of Aksoy Yazici, Murphy, Rudnev and Shkredov (2016) on the number
of solutions of certain equations involving products and differences of sets in prime finite …

Let f:F_q^l→F_q be a given function. We say that f is a moderate expander if there exists an
ϵ>0 such that for |A|\gtrsimq^1-ϵ one has that |f(A,...,A)|\gtrsimq. We show that x_1x_2+(x_3 …

In this paper, we use methods from spectral graph theory to obtain some results on the sum–
product problem over finite valuation rings R of order qr which generalize recent results …

Additive Combinatorics over Finite Fields: New Results and Applications. Page 245 Igor E.
Shparlinski Additive Combinatorics over Finite Fields: New Results and Applications Abstract …

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Using graph spectra, we give a new proof of a statement of Shparlinski which was the main
tool in the estimation of the energy of a distance set and we derive some consequence of it …

Note on character sums of Hilbert cubes - ScienceDirect Skip to main contentSkip to article
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We prove various low-energy decomposition results, showing that we can decompose a
finite set $ A\subset\mathbb {F} _p $ satisfying $| A|< p^{5/8} $, into $ A= S\sqcup T $ so that …

We extend a result due to Bourgain on the uniform distribution of residues by proving that
subsets of the type $ f (I)\cdot H $ are equidistributed (as $ p $ tends to infinity), where $ f $ is …

For sufficiently large subsets $\mathcal {A},\mathcal {B},\mathcal {C},\mathcal {D} $ of
$\mathbb {F} _q $, Gyarmati and Sárközy (2008) showed the solvability of the equations …