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Hecke groups $H (λ_{q})$ are the discrete subgroups of $P S L (2, ℝ)$ generated by $S (z) = - {(z + λ_{q})}^{- 1}$ and $T (z) = - \frac{1}{z}$ . The commutator subgroup of $H$ ( $λ_{q})$ , denoted by $H^{'} (λ_{q})$ , is studied in [2]. It was shown that $H^{'} (λ_{q})$ is a free group of rank $q - 1$ . Here the extended Hecke groups $\bar{H} (λ_{q})$ , obtained by adjoining $R_{1} (z) = 1 / \bar{z}$ to the generators of $H (λ_{q})$ , are considered. The commutator subgroup of $\bar{H} (λ_{q})$ is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the $H (λ_{q})$ case, the index of $H^{'} (λ_{q})$ is changed by $q$ , in the case of $\bar{H} (λ_{q})$ , this number is either 4 for...

Compactifications de l'espace de modules de Hilbert-Blumenthal

M. Rapoport (1978)

Compositio Mathematica

Companion forms and Kodaira-Spencer theory.

José Felipe Voloch, Robert F. Coleman (1992)

Inventiones mathematicae

Companion forms and weight one forms.

Buzzard, Kevin, Taylor, Richard (1999)

Annals of Mathematics. Second Series

Compatible families of elliptic type

David E. Rohrlich (2010)

Acta Arithmetica

Completely normal elements in some finite abelian extensions

Ja Koo, Dong Shin (2013)

Open Mathematics

We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.

Computation of $p$ -adic heights and log convergence.

Mazur, Barry, Stein, William, Tate, John (2007)

Documenta Mathematica

Computations of Galois representations associated to modular forms of level one

Peng Tian (2014)

Acta Arithmetica

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 uper bound on...

Computing fundamental domains for Fuchsian groups

John Voight (2009)

Journal de Théorie des Nombres de Bordeaux

We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group $Γ$ with cofinite area. As a consequence, we compute the invariants of $Γ$ , including an explicit finite presentation for $Γ$ .

Computing Hecke eigenvalues below the cohomological dimension.

Gunnells, Paul E. (2000)

Experimental Mathematics

Computing modular degrees using $L$ -functions

Christophe Delaunay (2003)

Journal de théorie des nombres de Bordeaux

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.

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Cohomology of torus bundles over Kuga fiber varieties.

Cohomology of Vector-Valued Automorphic Forms.

Cohomology sets inside arithmetic groups

Coleman power series for $K_{2}$ and $p$ -adic zeta functions of modular forms.

Comment distribuer des points uniformément sur une sphère ? (D'après Lubotzky, Phillips et Sarnak)

Commutator subgroups of the extended Hecke groups $\bar{H} (λ_{q})$