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arXiv · 2407.00532

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

June Kayath·Connor Lane·Ben Neifeld·Tianyu Ni·Hui Xue
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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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June Kayath, Connor Lane, Ben Neifeld, Tianyu Ni, Hui Xue. 2024-06-29. Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values. https://arxiv.org/abs/2407.00532

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