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math.CO2009
Sum-product inequalities with perturbation
Spencer Backman, Ernie Croot, Derrick Hart +1
Suppose that A is a set of n real numbers, each at least 1 apart. Define the ``perturbed sum and product sets'' S and P to be the sums a + b + f(a,b) and products (a+g(a,b))(b+h(a,…
math.CO2009
k-fold sums from a set with few products
Ernie Croot, Derrick Hart
In the present paper we show that if A is a set of n real numbers, and the product set A.A has at most n^(1+c) elements, then the k-fold sumset kA has at least n^(log(k/2)/2 log 2…