Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911260975562752 |
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| author | Lin, Hua Wong, Peng-Jie |
| author_facet | Lin, Hua Wong, Peng-Jie |
| contents | A famous conjecture of Keating and Snaith asserts that central values of $L$-functions in a given family admit a log-normal distribution with a prescribed mean and variance depending on the symmetry type of the family. Based on a recent work of Radziwill and Soundararajan, we obtain a conditional lower bound towards Keating-Snaith's conjecture for a "thin" family of cubic Hecke $L$-functions over the Eisenstein field. A key new input is certain twisted estimates of the 1-level density of zeros of cubic Hecke $L$-functions, extending the previous work of David and Güloğlu, under the Generalised Riemann Hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field Lin, Hua Wong, Peng-Jie Number Theory 11M06 (Primary) 11M41 (Secondary) A famous conjecture of Keating and Snaith asserts that central values of $L$-functions in a given family admit a log-normal distribution with a prescribed mean and variance depending on the symmetry type of the family. Based on a recent work of Radziwill and Soundararajan, we obtain a conditional lower bound towards Keating-Snaith's conjecture for a "thin" family of cubic Hecke $L$-functions over the Eisenstein field. A key new input is certain twisted estimates of the 1-level density of zeros of cubic Hecke $L$-functions, extending the previous work of David and Güloğlu, under the Generalised Riemann Hypothesis. |
| title | Towards Keating-Snaith's conjecture for cubic Hecke $L$-functions over the Eisenstein field |
| topic | Number Theory 11M06 (Primary) 11M41 (Secondary) |
| url | https://arxiv.org/abs/2511.08783 |