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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 $Q_{5} (\sqrt[4]{5}, \sqrt{3})$ .

On the Supercuspidal Represewntations of SL2 and ist Two-fold Cover. II.

David Manderscheid (1984)

Mathematische Annalen

On the Supercuspidal Represewntations of SL2 and ist Two-fold Cover. I

David Manderscheid (1984)

Mathematische Annalen

On Torsion in the Cohomology of Certain S-arithmetic Groups.

Stefan Kühnlein (1994)

Manuscripta mathematica

On values of a modular form on Γ₀(N)

D. Choi (2006)

Acta Arithmetica

Optimal levels for modular mod 2 representations over totally real fields.

Jarvis, Frazer (2007)

Documenta Mathematica

Ordinary $p$ -adic Eisenstein series and $p$ -adic $L$ -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for ${GL}_{2} \times 𝒦^{\times}$ by the method of Eisenstein congruence on $G U (3, 1)$ , where $𝒦$ is an imaginary quadratic field. We construct a $p$ -adic family of ordinary Eisenstein series on the group of unitary similitudes $G U (3, 1)$ with the optimal constant term which is basically the product of the Kubota-Leopodlt $p$ -adic $L$ -function and a $p$ -adic $L$ -function for ${GL}_{2} \times 𝒦^{\times}$ . This construction also provides a different point of view of $p$ -adic...

Overconvergent modular forms

Vincent Pilloni (2013)

Annales de l’institut Fourier

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.

$p$ -adic $L$ -functions for modular forms

Shai Haran (1987)

Compositio Mathematica

$p$ -adic $L$ -functions for unitary Shimura varieties. I: Construction of the Eisenstein measure.

Harris, Michael, Li, Jian-Shu, Skinner, Christopher M. (2007)

Documenta Mathematica

$p$ -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

We study the critical values of the complex standard- $L$ -function attached to a holomorphic Siegel modular form and of the twists of the $L$ -function by Dirichlet characters. Our main object is for a fixed rational prime number $p$ to interpolate $p$ -adically the essentially algebraic critical $L$ -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence of...

$p$ -adic ordinary Hecke algebras for $GL (2)$

Haruzo Hida (1994)

Annales de l'institut Fourier

We study the $p$ -adic nearly ordinary Hecke algebra for cohomological modular forms on $G L (2)$ over an arbitrary number field $F$ . We prove the control theorem and the independence of the Hecke algebra from the weight. Thus the Hecke algebra is finite over the Iwasawa algebra of the maximal split torus and behaves well under specialization with respect to weight and $p$ -power level. This shows the existence and the uniqueness of the (nearly ordinary) $p$ -adic analytic family of cohomological Hecke eigenforms...

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Displaying 81 – 100 of 125

On the non-existence of simple congruences for quotients of Eisenstein series

On the p-adic Eichler-Shimura isomorphism for ...-adic cusp forms.

On the rationality of periods of primitive forms

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

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