On Galois representations associated to Hilbert modular forms.
Frazer Jarvis (1997)
Journal für die reine und angewandte Mathematik
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Frazer Jarvis (1997)
Journal für die reine und angewandte Mathematik
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Cassou-Noguès, Philippe, Jehanne, Arnaud (1996)
Experimental Mathematics
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H. Hida (1986)
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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...
Rajender Adibhatla, Jayanta Manoharmayum (2012)
Acta Arithmetica
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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, -adic Galois representations associated to holomorphic Hilbert modular newforms.
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...
Nigel Boston (1991)
Inventiones mathematicae
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Y. Ihara (1986)
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Michael A. Bennett, Imin Chen, Sander R. Dahmen, Soroosh Yazdani (2014)
Acta Arithmetica
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We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.
Adam Logan (2002)
Acta Arithmetica
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Peder Frederiksen, Ian Kiming (2004)
Acta Arithmetica
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Wintenberger, J.-P. (2007)
Documenta Mathematica
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