https://scholars.lib.ntu.edu.tw/handle/123456789/624831
標題: | The derivative formula of p-adic L-functions for imaginary quadratic fields at trivial zeros | 作者: | Chida M Hsieh M.-L. MING-LUN HSIEH |
關鍵字: | L-functions; Modular forms; p-adic; Trivial zeros | 公開日期: | 2022 | 來源出版物: | Annales Mathematiques du Quebec | 摘要: | 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 + ε specialization. © 2022, Fondation Carl-Herz and Springer Nature Switzerland AG. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85128365300&doi=10.1007%2fs40316-022-00198-6&partnerID=40&md5=deb9a264cfd4a3741a1c9d7708bc1aab https://scholars.lib.ntu.edu.tw/handle/123456789/624831 |
ISSN: | 21954755 | DOI: | 10.1007/s40316-022-00198-6 |
顯示於: | 數學系 |
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