Families of modular forms
type: Item
instance of: scholarly article
title: Families of modular forms
zbMATH Open document ID: 1052.11036
author: Kevin Buzzard
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2004-08-05T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/222526
full work available at URL: jtnb13-1 english.html
review text: The author gives a down-to-earth introduction to the theory of \(p\)-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the \(U_p\)-operator acting on \(S_k(\Gamma_1(N_p))\) is bounded below by an explicit quadratic lower bound which is independent of \(k\) (Theorem 3).
reviewed by: Andrzej Dąbrowski
Mathematics Subject Classification ID: 11F85
Mathematics Subject Classification ID: 11F11
zbMATH DE Number: 2081346
zbMATH Keywords: \(p\)-adic family of modular forms
zbMATH Keywords: \(U_p\) operator
zbMATH Keywords: Newton polygon
MaRDI profile type: Publication
OpenAlex ID: W2097036406
cites work: \(p\)-adic Banach spaces and families of modular forms
cites work: Q4249385
cites work: Families of Modular Eigenforms
cites work: Q4875376
cites work: Q4317836
cites work: Dimension variation of classical and \(p\)-adic modular forms
DOI: 10.5802/JTNB.302
description: scientific article; zbMATH DE number 2081346