Co-periods and central symmetric cube L-values
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909698346713088 |
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| author | Cai, Li Fan, Yangyu She, Dongming |
| author_facet | Cai, Li Fan, Yangyu She, Dongming |
| contents | In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the central critical value of symmetric cube $L$-functions. We also deduce from the local multiplicity one result that there exist cuspidal automorphic forms with prescribed local components and non-vanishing central symmetric cube $L$-values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Co-periods and central symmetric cube L-values Cai, Li Fan, Yangyu She, Dongming Number Theory In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the central critical value of symmetric cube $L$-functions. We also deduce from the local multiplicity one result that there exist cuspidal automorphic forms with prescribed local components and non-vanishing central symmetric cube $L$-values. |
| title | Co-periods and central symmetric cube L-values |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.15279 |