This questions concerns section 12.2, page 408 of Peskin and Schroeder's quantum field theory book. Among renormalization conditions listed in Eq. 12.30, the first one requires that self-energy correction for the scalar field be equal to zero at $p^2=-M^2$, where $M$ is the renormalization point. But should it not require instead that the self-energy correction be equal to zero at $p^2=0$, rather than at some unphysical point? Is this not the definition of masslessness? Moreover, in the rest of the section the authors act as if they used this latter definition and not the one dispayed in Eq. 12.30. So I am a little bit confused. Have the authors made a mistake?
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