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Modular forms of weight 1/2 over class number 1 imaginary quadratic number fields. (English) Zbl 0787.11014
In the important paper [J.-P. Serre and H. Stark, Lect. Notes Math. 627, 27-67 (1977; Zbl 0371.10029)] it was proved that the space of modular forms of weight 1/2 on $$\Gamma_ 0(N)$$ $$(4\mid N)$$ is spanned by theta functions. Using representation-theoretic methods this result was later generalized to arbitrary ground fields in [S. Gelbart and I. I. Piatetski-Shapiro, Invent. Math. 59, 145-188 (1980; Zbl 0426.10027)].
In the present paper the author generalizes the original proof of Serre and Stark to forms of weight 1/2 over the nine imaginary quadratic number fields having class number 1.
##### MSC:
 11F37 Forms of half-integer weight; nonholomorphic modular forms
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