26 citations · 89 across the 23 of their papers we have counts for
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math.NT2008★ 3 cited
Sets of integers that do not contain long arithmetic progressions
Kevin O'Bryant
In 1946, Behrend gave a construction of dense finite sets of integers that do not contain 3-term arithmetic progressions. In 1961, Rankin generalized Behrend's construction to sets…
math.NT2008
Can you hear the shape of a Beatty sequence?
Ron Graham, Kevin O'Bryant
Let K(x_1,...,x_d) be a polynomial. If you are not given the real numbers α_1, α_2, ...,α_d, but are given the polynomial K and the sequence a_n=K(\floor{nα_1},\floor{nα_2},...,\fl…
math.CA2008
The supremum of autoconvolutions, with applications to additive number theory
Greg Martin, Kevin O'Bryant
We adapt a number-theoretic technique of Yu to prove a purely analytic theorem: if f(x) is in L^1 and L^2, is nonnegative, and is supported on an interval of length I, then the sup…