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| Format: | Preprint |
| Veröffentlicht: |
2019
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| Online-Zugang: | https://arxiv.org/abs/1905.00792 |
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| _version_ | 1866929438685396992 |
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| author | Andreatta, Fabrizio Iovita, Adrian |
| author_facet | Andreatta, Fabrizio Iovita, Adrian |
| contents | For every triple F,K,p where F is a classical elliptic eigenform, K is a quadratic imaginary field and p> 3 is a prime integer which is not split in K, we attach a p-adic L function which interpolates the algebraic parts of the special values of the complex L-functions of F twisted by certain algebraic Hecke characters of K. This construction extends a classical construction of N. Katz, for F an Eisenstein series and of Bertolini-Darmon-Prasana, for F a cuspform, when p is split in K.
Moreover we prove a Kronecker limit formula, respectively p-adic Gross-Zagier formulae for our newly defined p-adic L-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_00792 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Katz type p-adic L-functions for primes p non-split in the CM field Andreatta, Fabrizio Iovita, Adrian Number Theory 11F67, 11F33, 11G15 For every triple F,K,p where F is a classical elliptic eigenform, K is a quadratic imaginary field and p> 3 is a prime integer which is not split in K, we attach a p-adic L function which interpolates the algebraic parts of the special values of the complex L-functions of F twisted by certain algebraic Hecke characters of K. This construction extends a classical construction of N. Katz, for F an Eisenstein series and of Bertolini-Darmon-Prasana, for F a cuspform, when p is split in K. Moreover we prove a Kronecker limit formula, respectively p-adic Gross-Zagier formulae for our newly defined p-adic L-functions. |
| title | Katz type p-adic L-functions for primes p non-split in the CM field |
| topic | Number Theory 11F67, 11F33, 11G15 |
| url | https://arxiv.org/abs/1905.00792 |