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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2306.07039 |
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| _version_ | 1866909439580176384 |
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| author | Liu, Yifeng |
| author_facet | Liu, Yifeng |
| contents | We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number is $+1$, the construction relies on global Bessel periods on definite unitary groups which, due to the recent advances on the global Gan--Gross--Prasad conjecture, interpolate classical central $L$-values. When the root number is $-1$, we construct an element in the Iwasawa Selmer group using the diagonal cycle on the product of unitary Shimura varieties, and conjecture that its $p$-adic height interpolates derivatives of cyclotomic $p$-adic $L$-functions. We also propose the nonvanishing conjecture and the main conjecture in both cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07039 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anticyclotomic $p$-adic $L$-functions for Rankin--Selberg product Liu, Yifeng Number Theory We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number is $+1$, the construction relies on global Bessel periods on definite unitary groups which, due to the recent advances on the global Gan--Gross--Prasad conjecture, interpolate classical central $L$-values. When the root number is $-1$, we construct an element in the Iwasawa Selmer group using the diagonal cycle on the product of unitary Shimura varieties, and conjecture that its $p$-adic height interpolates derivatives of cyclotomic $p$-adic $L$-functions. We also propose the nonvanishing conjecture and the main conjecture in both cases. |
| title | Anticyclotomic $p$-adic $L$-functions for Rankin--Selberg product |
| topic | Number Theory |
| url | https://arxiv.org/abs/2306.07039 |