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In the complex Langevin approach to lattice simulations at nonzero density,zeroes of the fermion determinant lead to a meromorphic drift and hence a needto revisit the theoretical derivation. We discuss how poles in the drift affectthe formal justification of the approach and then explore the various potentialissues in simple models, in a manner that is applicable to heavy dense and fullQCD.

On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models