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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)).…
math.NT2002
On the Oscillations of Multiplicative Functions Taking Values +/- 1
Ernie Croot
For completely multiplicative functions f(n) taking values 1 and -1, under certain conditions on f(n) we show that f(n) changes sign at least x exp(-7(log log x)sqrt(log x)) times…