On the equation a³ + b³ⁿ = c²

Michael A. Bennett; Imin Chen; Sander R. Dahmen; Soroosh Yazdani

Displaying similar documents to “On the equation a³ + b³ⁿ = c²”

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...

On modular representations of Gal (.../Q) arising from modular forms.

K.A. Ribet (1990)

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On Galois representations arising from towers of coverings of P1 ... .

Y. Ihara (1986)

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An infinite ferm in the universal deformation space of Galois representations.

B. Mazur (1997)

Collectanea Mathematica

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I hope this article will be helpful to people who might want a quick overview of how modular representations fit into the theory of deformations of Galois representations. There is also a more specific aim: to sketch a construction of a point-set topological'' configuration (the image of an infinite fern'') which emerges from consideration of modular representations in the universal deformation space of all Galois representations. This is a configuration hinted previously, but now, thanks...

Coupling of universal monodromy representations of Galois-Teichmüller modular groups.

Hiroaki Nakamura (1996)

Mathematische Annalen

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Multiplicities of mod p Galois representations.

Chandrashekhar Khare (1998)

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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.