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Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values

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arxiv 2407.00532 v1 pith:GXG3A3DK submitted 2024-06-29 math.NT

classification math.NT
keywords eigenformsnonvanishingcentralgeneratedheckesubspacesubspacestwisted
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abstract

In this paper, we construct explicit spanning sets for two spaces. One is the subspace generated by integral-weight Hecke eigenforms with nonvanishing quadratic twisted central $L$-values. The other is a subspace generated by half-integral weight Hecke eigenforms with certain nonvanishing Fourier coefficients. Along the way, we show that these subspaces are isomorphic via the Shimura lift.

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