Let E k (z) be the normalized Eisenstein series of weight k for the full modular group S L(2, Z). Let a > 0 be an even integer. In this paper we completely determine when the zeros of E k interlace with the zeros of E k+a . This generalizes a result of Nozaki on the interlacing of zeros of E k and E k+12 .
We examine virtual resolutions of Stanley-Reisner ideals for a product of projective spaces. In particular, we provide sufficient conditions for a simplicial complex to be virtually Cohen-Macaulay (to have a virtual resolution with length equal to its codimension). We also show that all balanced simplicial complexes are virtually Cohen-Macaulay.
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