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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2604.10818 |
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| _version_ | 1866914467276652544 |
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| author | Tsang, Kin Ming |
| author_facet | Tsang, Kin Ming |
| contents | Let $π$ be a cuspidal automorphic representation for $\mathrm{GL}(n)$ over a number field. We establish a conditional upper bound on the number of cuspidal isobaric summands in the symmetric $k$-th power lift of $π$, assuming that the symmetric $m$-th power lift of $π$ is automorphic and cuspidal for all $m \leq k-1$, along with other specified Langlands functoriality conjectures. For sufficiently large $k$, the resulting bound is independent of the specific value of $k$. We further extend our study to cases in which the cuspidality assumptions on the symmetric power lifts are relaxed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conjectural decomposition of symmetric powers of automorphic representations for $\mathrm{GL}(n)$ Tsang, Kin Ming Number Theory 11F70 Let $π$ be a cuspidal automorphic representation for $\mathrm{GL}(n)$ over a number field. We establish a conditional upper bound on the number of cuspidal isobaric summands in the symmetric $k$-th power lift of $π$, assuming that the symmetric $m$-th power lift of $π$ is automorphic and cuspidal for all $m \leq k-1$, along with other specified Langlands functoriality conjectures. For sufficiently large $k$, the resulting bound is independent of the specific value of $k$. We further extend our study to cases in which the cuspidality assumptions on the symmetric power lifts are relaxed. |
| title | Conjectural decomposition of symmetric powers of automorphic representations for $\mathrm{GL}(n)$ |
| topic | Number Theory 11F70 |
| url | https://arxiv.org/abs/2604.10818 |