We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2,Z) in terms of theta series. We apply this general setup to obtain closed and easily computable formulas for conformal characters of rational models of W-algebras. 2 Université Bordeaux I, UFR de Mathématiques et Informatiques, 351 rue de la Libération, 3340...

We prove a q-analog of a classical binomial congruence due to Ljunggren which states that ap bp ! ≡ a b ! modulo p for primes p > 5. This congruence subsumes and builds on earlier congruences by Babbage, Wolstenholme and Glaisher for which we recall existing q-analogs. Our congruence generalizes an earlier result of Clark. Résumé. Nous démontrons un q-analogue d’une congruence binomiale classiq...

The definition of open bisimilarity on the χ-processes does not give rise to a sensible relation on the χ-processes with the mismatch operator. The paper proposes ground open congruence as a principal open congruence on the χ-processes with the mismatch operator. The algebraic properties of the ground congruence is studied. The paper also takes a close look at barbed congruence. This relation i...

We used West and Kenny's (2011) Truth-and-Bias (T&B) model to examine how accurately group therapists' judge their group members' alliances, and the effects of therapist-patient congruence in alliance ratings on patient outcomes. Were considered: (a) directional bias - therapists' tendency to over- or underrate their clients' alliances, (b) truth strength - clients' alliance ratings, and (c) bi...

Definitions and classifications of reduced surds for non-arithmetical groups on the hyperbolic plane is proposed, as well those some congruence subgroups. The considered are desymmetrized group, its Γ0 subgroup, a generalized Hecke group according choice commutator subgroup group. definitions studied to ordering generators conjugacy subclasses groups. construction tori defined obtained after te...

In this paper, we study the combinatorics of congruence subgroups modular group by generalizing results obtained in non-modular case. For this, define a notion irreducible solutions from which can build all solutions. particular, give particular solution, for any N, and list N?6.

Let X be a locally symmetric space defined by simple Chevalley group G and congruence subgroup of G(Q). In this generality, the Weyl law for was proved Lindenstrauss Venkatesh. case where is simply connected, we sharpen their result giving power-saving estimate remainder term.

We describe quantum symmetries associated with the F 4 Dynkin diagram. Our study stems from an analysis of the (Ocneanu) modular splitting equation applied to a partition function which is invariant under a particular congruence subgroup of the modular group.

Let O 1 be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order O in an indeenite quaternion division algebra over Q. Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for O 1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian deened on the Maaa newforms for the Hecke...