The conjecture is still open, and the best result to date is due to Solymosi [S], who showed that max(|A + A|, |AA|) â‰¥ C |A| 14 11âˆ’ . In the finite field setting this situation is much moreâ€¦ (More)

Let Fp be the field of a prime order p. For a subset A âŠ‚ Fp we consider the product set A(A + 1). This set is an image of A Ã— A under the polynomial mapping f(x, y) = xy + x : Fp Ã— Fp â†’ Fp. In theâ€¦ (More)

In this paper the authors study set expansion in finite fields. Fourier analytic proofs are given for several results recently obtained by Solymosi ([33]), Vu ([41]) and Vinh ([40]) using spectralâ€¦ (More)

In this paper we study extension theorems associated with general varieties in two dimensional vector spaces over finite fields. Applying Bezoutâ€™s theorem, we obtain the sufficient and necessaryâ€¦ (More)

Let A = (aj,k)j,kâ‰¥1 be a non-negative matrix. In this paper, we characterize those A for which â€–Aâ€–E,F are determined by their actions on decreasing sequences, where E and F are suitable normed Rieszâ€¦ (More)

Let A = (aj,k)j,kâ‰¥1 be a non-negative matrix. In this paper, we characterize those A for which â€–Aâ€–lp,lq are determined by their actions on non-negative decreasing sequences, where one of p and q is 1â€¦ (More)

In this paper we study the generalized ErdÃ¶s-Falconer distance problems in the finite field setting. The generalized distances are defined in terms of polynomials, and various formulas for sizes ofâ€¦ (More)

Let A be a subset of F = F p k , the field of p k elements with p prime. We let A + A = {a + b : a âˆˆ A, b âˆˆ A}, and AA = {ab : a âˆˆ A, b âˆˆ A}. It is fun (and useful) to prove lower bounds onâ€¦ (More)