On the slopes of the ${U_5}$ operator acting on overconvergent modular forms

L. J. P Kilford

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 $| | y^{κ / 2} {f ̃ | |}_{\infty} ≪_{ε, κ} N^{1 / 2 - 1 / 18 + ε} | | y^{κ / 2} f ̃ {| |}_{L^{2}}$ for a modular form f̃ of level 4N and weight κ, a half-integer.

Classical and overconvergent modular forms

Robert F. Coleman (1995)

Journal de théorie des nombres de Bordeaux

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

Toshiyuki Kikuta (2012)

Acta Arithmetica

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The 2-adic eigencurve is proper.

Buzzard, Kevin, Calegari, Frank (2007)

Documenta Mathematica

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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.

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 $k$ ?

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

Displaying similar documents to “On the slopes of the $U_{5}$ operator acting on overconvergent modular forms”