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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.03034 |
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| _version_ | 1866910750542397440 |
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| author | Hamieh, Alia Wong, Peng-Jie |
| author_facet | Hamieh, Alia Wong, Peng-Jie |
| contents | In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of adélic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances supporting the conjecture and extending the works of Iwaniec-Luo-Sarnak and many others. For applications, we obtain an upper bound for the average order of $L$-functions of Hilbert modular forms at $s=\frac{1}{2}$ as well as a positive proportion of non-vanishing of certain Rankin-Selberg $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low-Lying Zeros of $L$-functions of Adélic Hilbert Modular Forms and their Convolutions Hamieh, Alia Wong, Peng-Jie Number Theory In this article, we study the density conjecture of Katz and Sarnak for $L$-functions of adélic Hilbert modular forms and their convolutions. In particular, under the generalised Riemann hypothesis, we establish several instances supporting the conjecture and extending the works of Iwaniec-Luo-Sarnak and many others. For applications, we obtain an upper bound for the average order of $L$-functions of Hilbert modular forms at $s=\frac{1}{2}$ as well as a positive proportion of non-vanishing of certain Rankin-Selberg $L$-functions. |
| title | Low-Lying Zeros of $L$-functions of Adélic Hilbert Modular Forms and their Convolutions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.03034 |