Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918356797358080 |
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| author | Kumar, Sumit Mallesham, K. Panigrahy, Suraj |
| author_facet | Kumar, Sumit Mallesham, K. Panigrahy, Suraj |
| contents | For $M_1$ and $ M_2$ two distinct primes, let $ H_k^\star(M_1M_2, ψ)$ denote the set of primitive newforms of level $M_1M_2$, weight $k\geq 3$ and Nebentypus $ψ$ of conductor $M_1$. Let $π$ be a fixed $SL(3, \mathbb{Z})$ Hecke cusp form. We prove a Lindelöf--consistent upper bound for the second moment
\[ \mathop{ \sum_{\substack{ψ(M_1) \\ ψ(-1)=(-1)^k }}} \sideset{}{^h}\sum_{f \in H_k^{\star}(M_1M_2,ψ)} |L(1/2, π\times f)|^2 \ll_{π,ε} M_1^{1+ε}\]
in the range $M_2\leq M_1^{1+ε}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22127 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions Kumar, Sumit Mallesham, K. Panigrahy, Suraj Number Theory For $M_1$ and $ M_2$ two distinct primes, let $ H_k^\star(M_1M_2, ψ)$ denote the set of primitive newforms of level $M_1M_2$, weight $k\geq 3$ and Nebentypus $ψ$ of conductor $M_1$. Let $π$ be a fixed $SL(3, \mathbb{Z})$ Hecke cusp form. We prove a Lindelöf--consistent upper bound for the second moment \[ \mathop{ \sum_{\substack{ψ(M_1) \\ ψ(-1)=(-1)^k }}} \sideset{}{^h}\sum_{f \in H_k^{\star}(M_1M_2,ψ)} |L(1/2, π\times f)|^2 \ll_{π,ε} M_1^{1+ε}\] in the range $M_2\leq M_1^{1+ε}$. |
| title | Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.22127 |