On elliptic Galois representations and genus-zero modular units

Julio Fernández; Joan-C. Lario

Displaying similar documents to “On elliptic Galois representations and genus-zero modular units”

On Minkowski units constructed by special values of Siegel modular functions

Takashi Fukuda, Keiichi Komatsu (2003)

Journal de théorie des nombres de Bordeaux

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Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field $k_{6}$ of $ℚ (e x p (2 π i / 5))$ modulo $6$ . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group $G (k_{6} / ℚ)$ for the special values. Futhermore we construct the full unit group of $k_{6}$ using modular and circular units under the GRH.

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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Polynomials of Galois representations attached to elliptic curves.

A. Reverter, N. Vila (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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On octahedral extensions of $ℚ$ and quadratic $ℚ$ -curves

Julio Fernández (2003)

Journal de théorie des nombres de Bordeaux

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We give a necessary condition for a surjective representation Gal $(\bar{ℚ} / ℚ) \to {PGL}_{2} (𝔽_{3})$ to arise from the $3$ -torsion of a $ℚ$ -curve. We pay a special attention to the case of quadratic $ℚ$ -curves.

On Galois representations defined by torsion points of modular elliptic curves

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

Compositio Mathematica

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On the equation $a^{2} + b^{2 p} = c^{5}$

Imin Chen (2010)

Acta Arithmetica

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Arithmetic of the modular function $j_{1, 4}$

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

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We find a generator $j_{1, 4}$ of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator $N (j_{1, 4})$ which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

A condition for the rationality of certain elliptic modular forms over primes dividing the level

Andrea Mori (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $f$ be a weight $k$ holomorphic automorphic form with respect to $Γ_{0} (N)$ . We prove a sufficient condition for the integrality of $f$ over primes dividing $N$ . This condition is expressed in terms of the values at particular $C M$ curves of the forms obtained by iterated application of the weight $k$ Maaß operator to $f$ and extends previous results of the Author.

Computing modular degrees using $L$ -functions

Christophe Delaunay (2003)

Journal de théorie des nombres de Bordeaux

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We give an algorithm to compute the modular degree of an elliptic curve defined over $ℚ$ . Our method is based on the computation of the special value at $s = 2$ of the symmetric square of the $L$ -function attached to the elliptic curve. This method is quite efficient and easy to implement.