Hilbert modular Eisenstein congruences of local origin
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911480128995328 |
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| author | Fretwell, Dan Roberts, Jenny |
| author_facet | Fretwell, Dan Roberts, Jenny |
| contents | Let $F$ be an arbitrary totally real field. Under weak conditions we prove the existence of certain Eisenstein congruences between parallel weight $k \geq 3$ Hilbert eigenforms of level $\mathfrak{mp}$ and Hilbert Eisenstein series of level $\mathfrak{m}$, for arbitrary ideal $\mathfrak{m}$ and prime ideal $\mathfrak{p}\nmid \mathfrak{m}$ of $\mathcal{O}_F$. Such congruences have their moduli coming from special values of Hecke $L$-functions and their Euler factors, and our results allow for the eigenforms to have non-trivial Hecke character. After this, we consider the question of when such congruences can be satisfied by newforms, proving a general result about this. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert modular Eisenstein congruences of local origin Fretwell, Dan Roberts, Jenny Number Theory Let $F$ be an arbitrary totally real field. Under weak conditions we prove the existence of certain Eisenstein congruences between parallel weight $k \geq 3$ Hilbert eigenforms of level $\mathfrak{mp}$ and Hilbert Eisenstein series of level $\mathfrak{m}$, for arbitrary ideal $\mathfrak{m}$ and prime ideal $\mathfrak{p}\nmid \mathfrak{m}$ of $\mathcal{O}_F$. Such congruences have their moduli coming from special values of Hecke $L$-functions and their Euler factors, and our results allow for the eigenforms to have non-trivial Hecke character. After this, we consider the question of when such congruences can be satisfied by newforms, proving a general result about this. |
| title | Hilbert modular Eisenstein congruences of local origin |
| topic | Number Theory |
| url | https://arxiv.org/abs/2411.06987 |