虚二次域在平凡零点处的p进l函数的导数公式

IF 0.5 Q3 MATHEMATICS

Annales Mathematiques du Quebec Pub Date : 2022-05-26 DOI:10.1007/s40316-022-00198-6

Masataka Chida, Ming-Lun Hsieh

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引用次数: 4

摘要

在Darmon Dasgupta Pollack和Ventullo的著作中，通过Hilbert模形式之间的Eisenstein同余，解决了Deligne–Ribet p-adic L-函数的秩一Gross猜想。本文的目的是通过CM形式和非CM形式之间的同余，证明附加在虚二次域上的Katz p-adic L-函数的Gross猜想的类似性。新的成分是应用p-adic Rankin–Selberg方法构建一个非CM Hida家族，该家族与\（1+\varepsilon\）特化的CM形式的Hida家族一致。

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The derivative formula of p-adic L-functions for imaginary quadratic fields at trivial zeros

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.

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来源期刊

Annales Mathematiques du Quebec MATHEMATICS-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： The goal of the Annales mathématiques du Québec (formerly: Annales des sciences mathématiques du Québec) is to be a high level journal publishing articles in all areas of pure mathematics, and sometimes in related fields such as applied mathematics, mathematical physics and computer science. Papers written in French or English may be submitted to one of the editors, and each published paper will appear with a short abstract in both languages. History: The journal was founded in 1977 as „Annales des sciences mathématiques du Québec”, in 2013 it became a Springer journal under the name of “Annales mathématiques du Québec”. From 1977 to 2018, the editors-in-chief have respectively been S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea. Les Annales mathématiques du Québec (anciennement, les Annales des sciences mathématiques du Québec) se veulent un journal de haut calibre publiant des travaux dans toutes les sphères des mathématiques pures, et parfois dans des domaines connexes tels les mathématiques appliquées, la physique mathématique et l''informatique. On peut soumettre ses articles en français ou en anglais à l''éditeur de son choix, et les articles acceptés seront publiés avec un résumé court dans les deux langues. Histoire: La revue québécoise “Annales des sciences mathématiques du Québec” était fondée en 1977 et est devenue en 2013 une revue de Springer sous le nom Annales mathématiques du Québec. De 1977 à 2018, les éditeurs en chef ont respectivement été S. Dubuc, R. Cléroux, G. Labelle, I. Assem, C. Levesque, D. Jakobson, O. Cornea.