We study the rational Picard group of the projectivized moduli space PM¯g(n) of holomorphic n-differentials on complex genus g stable curves. We define n- 1 natural classes in this Picard group that we call Prym-Tyurin classes. We express these classes as linear combinations of boundary divisors and the divisor of n-differentials with a double zero. We give two different proofs of this result, using two alternative approaches: an analytic approach that involves the Bergman tau function and its vanishing divisor and an algebro-geometric approach that involves cohomological computations on the universal curve.