Dihedral Galois representations and Katz modular forms.

Wiese, Gabor

Displaying similar documents to “Dihedral Galois representations and Katz modular forms.”

On Galois representations defined by torsion points of modular elliptic curves

P. Bayer, J. C. Lario (1992)

Compositio Mathematica

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Modularity of Galois representations

Chris Skinner (2003)

Journal de théorie des nombres de Bordeaux

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This paper is essentially the text of the author’s lecture at the 2001 Journées Arithmétiques. It addresses the problem of identifying in Galois-theoretic terms those two-dimensional, $p$ -adic Galois representations associated to holomorphic Hilbert modular newforms.

On $p$ -adic geometric representations of $G_{ℚ}$ .

Wintenberger, J.-P. (2007)

Documenta Mathematica

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Rational elliptic curves are modular

Bas Edixhoven (1999-2000)

Séminaire Bourbaki

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The Way to the Proof of Fermat’s Last Theorem

Gerhard Frey (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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Computing the level of a modular rigid Calabi-Yau threefold.

Dieulefait, Luis V. (2004)

Experimental Mathematics

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Modularity of fibres in rigid local systems.

Darmon, Henri (1999)

Annals of Mathematics. Second Series

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Computations of Galois representations associated to modular forms of level one

Peng Tian (2014)

Acta Arithmetica

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We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved...

Newforms, inner twists, and the inverse Galois problem for projective linear groups

Luis V. Dieulefait (2001)

Journal de théorie des nombres de Bordeaux

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We reformulate more explicitly the results of Momose, Ribet and Papier concerning the images of the Galois representations attached to newforms without complex multiplication, restricted to the case of weight $2$ and trivial nebentypus. We compute two examples of these newforms, with a single inner twist, and we prove that for every inert prime greater than $3$ the image is as large as possible. As a consequence, we prove that the groups $PGL (2, 𝔽_{ℓ^{2}})$ for every prime $(ℓ \equiv 3, 5 (mod 8), ℓ > 3)$ , and $PGL (2, 𝔽_{ℓ^{5}})$ for every prime $ℓ \neg \equiv 0 \pm 1 (mod 11); ℓ > 3)$ , are...

Refinement of Tate's discriminant bound and non-existence theorems for mod $p$ Galois representations.

Moon, Hyunsuk, Taguchi, Yuichiro (2003)

Documenta Mathematica

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New examples of modular rigid Calabi-Yau threefolds.

Matthias Schütt (2004)

Collectanea Mathematica

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The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.