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math.NT2021
On almost Cap sets in three variables and the multivariable Cap set problem
Alexander Fish, Dibyendu Roy
In this note we prove that almost cap sets , i.e., the subsets of that do not contain too many arithmetic progressions of length three, s…
math.NT2005
Liouville Random functions and normal sets
Alexander Fish
We define a random Liouville function (λ_Q) which depends on a random set (Q) of primes and prove that (A_Q = \{n \in \mathbb{N} | λ_Q(n) = -1 \}) is normal almost everywhere. This…