20 citations · 85 across the 30 of their papers we have counts for
7 papers · 1 filter
Convexity and a sum-product type estimate
Liangpan Li, Oliver Roche-Newton
In this paper we further study the relationship between convexity and additive growth, building on the work of Schoen and Shkredov (\cite{SS}) to get some improvements to earlier r…
On a theorem of Schoen and Shkredov on sumsets of convex sets
Liangpan Li
A set of reals labeled in increasing order is called convex if there exists a continuous strictly convex function such that for every . Given…
Multi-fold sums from a set with few products
Liangpan Li
In this paper we show that for any , there exist two universal constants , such that for any finite subset of positive real numbers with , $|k…
An improved sum-product estimate over finite fields
Liangpan Li, Oliver Roche-Newton
This paper gives an improved sum-product estimate for subsets of a finite field whose order is not prime. It is shown, under certain conditions, that $$\max\{|A+A|,|A\cdot{A}|\}\gg…
An improved sum-product estimate for general finite fields
Oliver Roche-Newton
This paper improves on a sum-product estimate obtained by Katz and Shen for subsets of a finite field whose order is not prime.
Collinear triples in permutations
Liangpan Li
Let be a permutation and be the number of collinear triples in the graph of , where denotes a finite field of elements.…