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math.CO2005★ 2 cited
The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit
Ernie Croot
Given a density t in (0,1], and a prime p, let S be any subset of F_p having at least tp elements, and having the least number of three-term arithmetic progressions mod p among all…
math.CO2002
On Non-intersecting Arithmetic Progressions
Ernie Croot
We prove that if one has k non-intersecting arithmetic progressions of integers, with common differences 2 <= q_1,...,q_k <= x, then k < x exp((-1/6 + o(1)) sqrt(log x loglog x)).…