Artin L-functions and modular forms associated to quasi-cyclotomic fields

Sunghan Bae; Yong Hu; Linsheng Yin

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Displaying similar documents to “Artin L-functions and modular forms associated to quasi-cyclotomic fields”

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...

The number of S₄-fields with given discriminant

Jürgen Klüners (2006)

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

K.A. Ribet (1990)

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The weight in Serre's conjectures on modular forms.

Bas Edixhoven (1992)

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Numerical calculation of twisted adjoint $L$ -values attached to modular forms.

Hiraoka, Yoshio (2000)

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Besser, Amnon (1997)

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

Dieulefait, Luis V. (2004)

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On the anticyclotomic main conjecture for CM fields.

H. Hida, J. Tilouine (1994)

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Higher congruence companion forms

Rajender Adibhatla, Jayanta Manoharmayum (2012)

Acta Arithmetica

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On values of a modular form on Γ₀(N)

D. Choi (2006)

Acta Arithmetica

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Distinguished Representations and Modular Forms of Half-integral Weight.

I.I. Piatetski-Shapiro, St. Gelbart (1980)

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On the equation a³ + b³ⁿ = c²

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.

Modular Forms Associated to Real Quadratic Fields.

Don Zagier (1975)

Inventiones mathematicae

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