The Harris-Venkatesh conjecture for derived Hecke operators III: local constants
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914821069340672 |
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| author | Zhang, Robin |
| author_facet | Zhang, Robin |
| contents | The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement with the Stark conjecture for imaginary dihedral modular forms of weight $1$. This paper explicitly describes the constants appearing in the Harris-Venkatesh (plus Stark) conjecture for dihedral modular forms by evaluating $\mathrm{GL}(2) \times \mathrm{GL}(2)$ Rankin--Selberg periods and zeta integrals on newforms and optimal forms. One consequence is a formula for the ratio between Petersson norms and adjoint $L$-values. Our calculations also extend to exotic modular forms whose level is odd or whose Deligne-Serre representation is $2$-ordinary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Harris-Venkatesh conjecture for derived Hecke operators III: local constants Zhang, Robin Number Theory 11F67 (Primary) 11F27, 11F41, 11F70, 11R42, 11S40 (Secondary) The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement with the Stark conjecture for imaginary dihedral modular forms of weight $1$. This paper explicitly describes the constants appearing in the Harris-Venkatesh (plus Stark) conjecture for dihedral modular forms by evaluating $\mathrm{GL}(2) \times \mathrm{GL}(2)$ Rankin--Selberg periods and zeta integrals on newforms and optimal forms. One consequence is a formula for the ratio between Petersson norms and adjoint $L$-values. Our calculations also extend to exotic modular forms whose level is odd or whose Deligne-Serre representation is $2$-ordinary. |
| title | The Harris-Venkatesh conjecture for derived Hecke operators III: local constants |
| topic | Number Theory 11F67 (Primary) 11F27, 11F41, 11F70, 11R42, 11S40 (Secondary) |
| url | https://arxiv.org/abs/2301.00612 |