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Alice
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Why can there be holomorphic modular forms of negative half integral weight?
Yes, I mean the specialization at $s=0$. In the paper, Shimura computed the Fourier expansion of $E^*(z,0)$. For positive weights, we can also see that $E(z,0)$ is holomorphic from formula (1.4). For the negative weights, which are used to give the integral representation of the adjoint lifting, Shimura claims a functional equation relating positive and negative weight at p.93. One can also from the formulas of Lemma 3, p.288, Elementary theory of L-function and Eisenstein series to see that $E(z,0)$ should be holomorphic for positive and negative weight.
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About quotient varieties
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About quotient varieties
My fault. Let me edit the post.
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