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We establish the first pointwise ergodic theorems along thin sets of primenumbers; a set with zero density with respect to the primes. For instance wewill be able to achieve this with the Piatetski-Shapiro primes. Our methodswill be robust enough to solve the ternary Goldbach problem for some thin setsof primes.

$\ell^p(\mathbb{Z})$ -- boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems