Report
The derivative formula of $p$-adic $L$-functions for imaginary quadratic fields at trivial zeros
| العنوان: | The derivative formula of $p$-adic $L$-functions for imaginary quadratic fields at trivial zeros |
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| المؤلفون: | Chida, Masataka, Hsieh, Ming-Lun |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | The rank one Gross conjecture for Deligne-Ribet $p$-adic $L$-functions was solved in works of Darmon-Dasgupta-Pollack and Ventullo by the Eisenstein congruence among Hilbert modular forms. The purpose of this paper is to prove an analogue of the Gross conjecture for the Katz $p$-adic $L$-functions attached to imaginary quadratic fields via the congruences between CM forms and non-CM forms. The new ingredient is to apply the $p$-adic Rankin-Selberg method to construct a non-CM Hida family which is congruent to a Hida family of CM forms at the $1+\varepsilon$ specialization. Comment: Final version. The reference numbers differ from the journal version. To appear in Annales Mathematiques du Quebec (Special birthday issue for Bernadette Perrin-Riou) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s40316-022-00198-6 |
| URL الوصول: | http://arxiv.org/abs/2205.14711 |
| رقم الانضمام: | edsarx.2205.14711 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s40316-022-00198-6 |
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