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- Liangpan Li, Oliver Roche-Newton
- SIAM J. Discrete Math.
- 2011

- Brandon Hanson, Ben Lund, Oliver Roche-Newton
- Finite Fields and Their Applications
- 2016

- Oliver Roche-Newton
- J. London Math. Society
- 2016

- Oliver Roche-Newton
- Symposium on Computational Geometry
- 2015

In this note it is established that, for any finite set A of real numbers, there exist two elements a, b ∈ A such that |(a+A)(b+A)| |A| 2 log |A| . In particular, it follows that |(A + A)(A + A)| |A| 2 log |A| . The latter inequality had in fact already been established in an earlier work of the author and Rudnev [8], which built upon the recent… (More)

- Brendan Murphy, Oliver Roche-Newton, Ilya D. Shkredov
- SIAM J. Discrete Math.
- 2015

- Antal Balog, Oliver Roche-Newton
- Discrete & Computational Geometry
- 2015

A variation on the sum-product problem seeks to show that a set which is defined by additive and multiplicative operations will always be large. In this paper, we prove new results of this type. In particular, we show that for any finite set A of positive real numbers, it is true that ∣ ∣ ∣ a + b c + d : a, b, c, d ∈ A }∣ ∣ ∣ ≥ 2|A|2 − 1. As a consequence… (More)

Let F be a field with positive odd characteristic p. We prove a variety of new sum-product type estimates over F . They are derived from the theorem that the number of incidences between m points and n planes in the projective three-space PG(3, F ), with m ≥ n = O(p), is O(m √ n+ km), where k denotes the maximum number of collinear planes. The main result… (More)

- Timothy G. F. Jones, Oliver Roche-Newton
- J. Comb. Theory, Ser. A
- 2013

- Orit E. Raz, Oliver Roche-Newton, Micha Sharir
- Discrete Mathematics
- 2015

- Antal Balog, Oliver Roche-Newton, Dmitry Zhelezov
- Electr. J. Comb.
- 2017

We prove several expanders with exponent strictly greater than 2. For any finite set A ⊂ R, we prove the following six-variable expander results: |(A−A)(A−A)(A−A)| |A| 2+ 1 8 log 17 16 |A| , ∣∣∣∣A+A A+A + AA ∣∣∣∣ |A| 2 17 log 16 17 |A| , ∣∣∣∣AA+AA A+A ∣∣∣∣ |A| 18 log |A| , ∣∣∣∣AA+A AA+A ∣∣∣∣ |A| 18 log |A| .