Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910508219629568 |
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| author | Kayath, June Lane, Connor Neifeld, Ben Ni, Tianyu Xue, Hui |
| author_facet | Kayath, June Lane, Connor Neifeld, Ben Ni, Tianyu Xue, Hui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values Kayath, June Lane, Connor Neifeld, Ben Ni, Tianyu Xue, Hui Number Theory 11F37, 11F67 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. |
| title | Subspaces spanned by eigenforms with nonvanishing twisted central $L$-values |
| topic | Number Theory 11F37, 11F67 |
| url | https://arxiv.org/abs/2407.00532 |