In mathematics, the modular group is the projective special linear group PSL ⁡ ( 2 , Z ) {\displaystyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2...

functional equation with respect to the group action of the modular group and a growth condition. The theory of modular forms has origins in complex analysis...

subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves X(Γ)...

setting in which congruence subgroups can be studied is that of the modular group ⁠ S L 2 ( Z ) {\displaystyle \mathrm {SL} _{2}(\mathbb {Z} )} ⁠. If...

The Volkswagen Group MQB platform is the company's strategy for shared modular design construction of its transverse, front-engine, front-wheel-drive...

well as the study of polynomials. The modular group may be realised as a quotient of the special linear group SL ⁡ ( 2 , Z ) {\displaystyle \operatorname...

name comes from the classical name modular group of this group, as in modular form theory. In string theory, modular invariance is an additional requirement...

In mathematics, the modular group representation (or simply modular representation) of a modular tensor category C {\displaystyle {\mathcal {C}}} is a...

to this group as the "modular group of order 16", as its lattice of subgroups is modular. In this article this group will be called the modular maximal-cyclic...

{R} )} . Furthermore, the modular group has trivial center, and thus the modular group is isomorphic to the quotient group of B 3 {\displaystyle B_{3}}...

In mathematics, a Picard modular group, studied by Picard (1881), is a group of the form SU(J,L), where L is a 3-dimensional lattice over the ring of...

group only being the orientation-preserving transformations. PGL and PSL can also be defined over a ring, with an important example being the modular...

mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight...

In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers...

are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series...

Paramodular group, a generalization of the Siegel modular group Siegel domain, a generalization of the Siegel upper half space Siegel modular form, a type...

modular group PSL(2, Z). Also closely related is the 2-fold covering group, Mp(2, R), a metaplectic group (thinking of SL(2, R) as a symplectic group)...

The Volkswagen Group MEB platform (German: Modularer E-Antriebs Baukasten, 'modular electric-drive toolkit') is a modular car platform for electric cars...

Equivalence in the sense of generating the same lattice is represented by the modular group: T : z ↦ z + 1 {\displaystyle T:z\mapsto z+1} represents choosing a...

{\displaystyle \mathbb {C} } . An important example of this type of group is the Picard modular group SU ⁡ ( 2 , 1 ; Z [ i ] ) {\displaystyle \operatorname {SU}...

This set forms a group, since the inverse of a matrix in Γ is again in Γ, as is the product of two matrices in Γ. The modular group acts on the collection...

of the congruence group Γ(2), and generates the function field of the corresponding quotient, i.e., it is a Hauptmodul for the modular curve X(2). Over...

The Volkswagen Group MLB platform is the company's platform strategy, announced in 2012, for shared modular construction of its longitudinal, front-engined...

topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface...

sublattices permuted by the modular group PSL(2, Z), which is based on changes of basis for Λ. Let j denote the elliptic modular function of Felix Klein....

Felix Klein's j-invariant or j function is a modular function of weight zero for the special linear group SL ⁡ ( 2 , Z ) {\displaystyle \operatorname {SL}...

the action of the modular group on a certain tessellation of the hyperbolic plane, it follows from this theory that the modular group is isomorphic to...

topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms...

In mathematics, a Hilbert modular form is a generalization of modular forms to functions of two or more variables. It is a (complex) analytic function...

compactification is acted on continuously by the modular group. In particular any element of the modular group has a fixed point in Thurston's compactification...