Displaying similar documents to “On the slopes of the  U 5 operator acting on overconvergent modular forms”

Overconvergent modular forms

Vincent Pilloni (2013)

Annales de l’institut Fourier

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We give a geometric definition of overconvergent modular forms of any p -adic weight. As an application, we reprove Coleman’s theory of p -adic families of modular forms and reconstruct the eigencurve of Coleman and Mazur without using the Eisenstein family.

Bounds on sup-norms of half-integral weight modular forms

Eren Mehmet Kıral (2014)

Acta Arithmetica

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Bounding sup-norms of modular forms in terms of the level has been the focus of much recent study. In this work the sup-norm of a half-integral weight cusp form is bounded in terms of the level: we prove that | | y κ / 2 f ̃ | | ∞ ≪ ε , κ N 1 / 2 - 1 / 18 + ε | | y κ / 2 f ̃ | | L 2 for a modular form f̃ of level 4N and weight κ, a half-integer.

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.

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.

Geometric and p -adic Modular Forms of Half-Integral Weight

Nick Ramsey (2006)

Annales de l’institut Fourier

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In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define p -adic modular forms of half-integral weight and to construct p -adic Hecke operators.

On the characteristic power series of the U operator

Fernando Q. Gouvêa, Barry Mazur (1993)

Annales de l'institut Fourier

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We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent p -adic modular forms of weight k vary p -adically continuously as functions of k . Are they in fact Iwasawa functions of k ?