103 citations · 370 across the 51 of their papers we have counts for
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Additive energy and the Falconer distance problem in finite fields
Doowon Koh, Chun-Yen Shen
We study the number of the vectors determined by two sets in d-dimensional vector spaces over finite fields. We observe that the lower bound of cardinality for the set of vectors c…
Harmonic analysis related to homogeneous varieties in three dimensional vector space over finite fields
Doowon Koh, Chun-Yen Shen
In this paper we study extension problems, averaging problems, and generalized Erdos-Falconer distance problems associated with arbitrary homogeneous varieties in three dimensional…
The generalized Erdos-Falconer distance problems in vector spaces over finite fields
Doowon Koh, Chun-Yen Shen
In this paper we study the generalized Erdos-Falconer distance problems in the finite field setting. The generalized distances are defined in terms of polynomials, and various form…
Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields
Doowon Koh, Chun-Yen Shen
In this paper we study extension theorems associated with general varieties in two dimensional vector spaces over finite fields. Applying Bezout's theorem, we obtain the sufficient…