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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2403.18382 |
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| _version_ | 1866909379246161920 |
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| author | Wong, Peng-Jie |
| author_facet | Wong, Peng-Jie |
| contents | In this article, we aim to establish a prototype result regarding lower bounds of (joint) distributions of central $L'$-values through extending a method of Radziwill and Soundararajan of proving conditional bounds for distributions of central $L$-values (via the one-level density of low-lying zeros of involving $L$-functions). To illustrate this, we give several conditional bounds towards joint distributions of central $L'$-values and orders of Tate-Shafarevich groups in rank-one families of quadratic twists. As an application, we derive a simultaneous non-vanishing result for central $L'$-values in families of quadratic twists of triples of holomorphic modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On distributions of $L'$-values and orders of Sha groups in families of quadratic twists Wong, Peng-Jie Number Theory Primary 11G40, Secondary 11F11, 11G05, 11M41 In this article, we aim to establish a prototype result regarding lower bounds of (joint) distributions of central $L'$-values through extending a method of Radziwill and Soundararajan of proving conditional bounds for distributions of central $L$-values (via the one-level density of low-lying zeros of involving $L$-functions). To illustrate this, we give several conditional bounds towards joint distributions of central $L'$-values and orders of Tate-Shafarevich groups in rank-one families of quadratic twists. As an application, we derive a simultaneous non-vanishing result for central $L'$-values in families of quadratic twists of triples of holomorphic modular forms. |
| title | On distributions of $L'$-values and orders of Sha groups in families of quadratic twists |
| topic | Number Theory Primary 11G40, Secondary 11F11, 11G05, 11M41 |
| url | https://arxiv.org/abs/2403.18382 |