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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2511.22644 |
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| _version_ | 1866918221438779392 |
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| author | Ye, Liyuan |
| author_facet | Ye, Liyuan |
| contents | In this paper, we extend the results of Michel-Venkatesh and Hu-Michel-Nelson to establish an upper bound for triple product and Rankin-Selberg L-functions of the form $$L(π_1 \otimes π_2 \otimes π_3,\frac{1}{2})\ll_{π_3,ε}C(π_1\otimesπ_2)^{\frac{1}{2} + ε} \left( \frac{C(π_1 \otimes π_2)}{C(π_2 \otimes π_2)}\right)^{-δ}$$ in the spectral aspect, allowing conductor dropping. In particular, we obtain a subconvexity bound when $π_1\otimesπ_2$ stays uniformly away from QUE-like case. The new ingredient is a stationary phase analysis of the analytic newvectors introduced by Jana and Nelson in \cite{JN19}, for both $\mathrm{PGL}_2(\mathbb{R})$ and $\mathrm{PGL}_2(\mathbb{C})$, which is applied to a test vector conjecture for local triple product periods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stationary phase analysis for analytic newvectors and application to subconvexity problems Ye, Liyuan Number Theory In this paper, we extend the results of Michel-Venkatesh and Hu-Michel-Nelson to establish an upper bound for triple product and Rankin-Selberg L-functions of the form $$L(π_1 \otimes π_2 \otimes π_3,\frac{1}{2})\ll_{π_3,ε}C(π_1\otimesπ_2)^{\frac{1}{2} + ε} \left( \frac{C(π_1 \otimes π_2)}{C(π_2 \otimes π_2)}\right)^{-δ}$$ in the spectral aspect, allowing conductor dropping. In particular, we obtain a subconvexity bound when $π_1\otimesπ_2$ stays uniformly away from QUE-like case. The new ingredient is a stationary phase analysis of the analytic newvectors introduced by Jana and Nelson in \cite{JN19}, for both $\mathrm{PGL}_2(\mathbb{R})$ and $\mathrm{PGL}_2(\mathbb{C})$, which is applied to a test vector conjecture for local triple product periods. |
| title | Stationary phase analysis for analytic newvectors and application to subconvexity problems |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.22644 |