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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations -
H. Hida (2006)
Hilbert Modular Forms and Iwasawa Theory
- Publisher
- Springer Journals
- Copyright
- Copyright © Fondation Carl-Herz and Springer Nature Switzerland AG 2022
- ISSN
- 2195-4755
- eISSN
- 2195-4763
- DOI
- 10.1007/s40316-022-00198-6
- Publisher site
- See Article on Publisher Site
Abstract
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\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$1+\varepsilon $$\end{document} specialization.
Journal
Annales mathématiques du Québec – Springer Journals
Published: Apr 1, 2023
Keywords: p-adic; L-functions; Trivial zeros; Modular forms; Primary 11F33; 11R23