On the computation of base-change lifts and lifts of Hida families
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908942267842560 |
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| author | Blanco-Chacón, Iván Dieulefait, Luis Haavikko, Antti |
| author_facet | Blanco-Chacón, Iván Dieulefait, Luis Haavikko, Antti |
| contents | We derive an explicit formula for the Hecke eigenvalues of a Hilbert modular form which is a base-change lift of a classical newform to a totally real Galois number field. We show that for a totally real abelian number field $F$ the $L$-function of a base-change lifted form can be factorized as a product of twisted $L$-functions over the characters of $F$. Moreover, we use the formula for the Hecke eigenvalues of a base-change lift to prove the existence of a base-change lift of a Hida family. In particular, we show that a Hida family of classical Hecke eigenforms can be lifted to a formal power series that specializes to the base-change lifts of the Hida family of classical cusp forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05618 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the computation of base-change lifts and lifts of Hida families Blanco-Chacón, Iván Dieulefait, Luis Haavikko, Antti Number Theory 11F30, 11F11, 11F80 We derive an explicit formula for the Hecke eigenvalues of a Hilbert modular form which is a base-change lift of a classical newform to a totally real Galois number field. We show that for a totally real abelian number field $F$ the $L$-function of a base-change lifted form can be factorized as a product of twisted $L$-functions over the characters of $F$. Moreover, we use the formula for the Hecke eigenvalues of a base-change lift to prove the existence of a base-change lift of a Hida family. In particular, we show that a Hida family of classical Hecke eigenforms can be lifted to a formal power series that specializes to the base-change lifts of the Hida family of classical cusp forms. |
| title | On the computation of base-change lifts and lifts of Hida families |
| topic | Number Theory 11F30, 11F11, 11F80 |
| url | https://arxiv.org/abs/2604.05618 |