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)...

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...

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...

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

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...

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

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...

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...

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}}...

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

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

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

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...

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

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...

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

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...

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...

\backslash \mathbb {H} ^{2}} , where Γ {\displaystyle \Gamma } is the modular group, the Selberg zeta-function is of special interest. For this special...

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

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...

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

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}...

Recherche Scientifique. OCLC 4615520. Émile Picard Medal Picard modular group Picard modular surface Picard horn Bregille Funicular Hadamard, J. (1942). "Emile...

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...

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

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)...