Classical and overconvergent modular forms

Robert F. Coleman

Displaying similar documents to “Classical and overconvergent modular forms”

Families of modular forms

Kevin Buzzard (2001)

Journal de théorie des nombres de Bordeaux

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We give a down-to-earth introduction to the theory of families of modular forms, and discuss elementary proofs of results suggesting that modular forms come in families.

A basis for the space of modular forms

Shinji Fukuhara (2012)

Acta Arithmetica

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A decomposition of the space of higher order modular cusp forms

Karen Taylor (2012)

Acta Arithmetica

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Second order modular forms

G. Chinta, N. Diamantis (2002)

Acta Arithmetica

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Modular Forms of Half-Integral Weight on ...0(4).

Winfried Kohnen (1980)

Mathematische Annalen

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An integrality criterion for elliptic modular forms

Andrea Mori (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $f$ be an elliptic modular form level of N. We present a criterion for the integrality of $f$ at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to $f$ the iterates of the Maaß differential operators.

On the Dimensions of Spaces of Siegel Modular Forms of Weight One.

J.-S. Li (1996)

Geometric and functional analysis

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On p-adic Siegel modular forms of non-real Nebentypus

Toshiyuki Kikuta (2012)

Acta Arithmetica

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On the finiteness of $S h$ for motives associated to modular forms.

Besser, Amnon (1997)

Documenta Mathematica

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On the slopes of the $U_{5}$ operator acting on overconvergent modular forms

L. J. P Kilford (2008)

Journal de Théorie des Nombres de Bordeaux

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We show that the slopes of the $U_{5}$ operator acting on 5-adic overconvergent modular forms of weight $k$ with primitive Dirichlet character $χ$ of conductor 25 are given by either $\{\frac{1}{4} \cdot ⌊\frac{8 i}{5}⌋ : i \in ℕ\} or \{\frac{1}{4} \cdot ⌊\frac{8 i + 4}{5}⌋ : i \in ℕ\},$ depending on $k$ and $χ$ . We also prove that the space of classical cusp forms of weight $k$ and character $χ$ has a basis of eigenforms for the Hecke operators $T_{p}$ and $U_{5}$ which is defined over $Q_{5} (\sqrt[4]{5}, \sqrt{3})$ .