$L$-functions for $\mathrm{Sp}(2n)\times\mathrm{GL}(k)$ via non-unique models
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910013205774336 |
|---|---|
| author | Jin, Yubo Yan, Pan |
| author_facet | Jin, Yubo Yan, Pan |
| contents | Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case $n=k=2$. We show that these new integrals unfold to non-unique models on $\mathrm{Sp}_{2n}$. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the $L$-functions for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$, generalizing a previous result of the second-named author on $\mathrm{Sp}_{4}\times\mathrm{GL}_2$ and a previous work of Piatetski-Shapiro and Rallis on $\mathrm{Sp}_{2n}\times\mathrm{GL}_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02544 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $L$-functions for $\mathrm{Sp}(2n)\times\mathrm{GL}(k)$ via non-unique models Jin, Yubo Yan, Pan Number Theory Representation Theory Primary 11F70, Secondary 11F55, 22E50, 22E55 Let $n$ and $k$ be positive integers such that $n$ is even. We derive new global integrals for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$ from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case $n=k=2$. We show that these new integrals unfold to non-unique models on $\mathrm{Sp}_{2n}$. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the $L$-functions for $\mathrm{Sp}_{2n}\times\mathrm{GL}_k$, generalizing a previous result of the second-named author on $\mathrm{Sp}_{4}\times\mathrm{GL}_2$ and a previous work of Piatetski-Shapiro and Rallis on $\mathrm{Sp}_{2n}\times\mathrm{GL}_1$. |
| title | $L$-functions for $\mathrm{Sp}(2n)\times\mathrm{GL}(k)$ via non-unique models |
| topic | Number Theory Representation Theory Primary 11F70, Secondary 11F55, 22E50, 22E55 |
| url | https://arxiv.org/abs/2303.02544 |