Orientation-preserving mapping class group of the torus
For a group whose lattice of subgroups is modular, see Iwasawa group.
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In mathematics, the modular group is the projective special linear group of 2 × 2 matrices with integer coefficients and determinant 1. The matrices A and −A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.
In mathematics, the modulargroup is the projective special linear group PSL ( 2 , Z ) {\textstyle \operatorname {PSL} (2,\mathbb {Z} )} of 2 × 2 matrices...
functional equation with respect to the group action of the modulargroup, and a growth condition. The theory of modular forms therefore belongs to complex...
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...
subgroup Γ of the modulargroup 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 modulargroup, studied by Picard (1881), is a group of the form SU(J,L), where L is a 3-dimensional lattice over the ring of...
{R} )} . Furthermore, the modulargroup has trivial center, and thus the modulargroup is isomorphic to the quotient group of B 3 {\displaystyle B_{3}}...
topology, the mapping class group of a surface, sometimes called the modulargroup or Teichmüller modulargroup, is the group of homeomorphisms of the surface...
The Volkswagen Group MQB platform is the company's strategy for shared modular design construction of its transverse, front-engine, front-wheel-drive...
of two copies of the upper half-plane by a Hilbert modulargroup. More generally, a Hilbert modular variety is an algebraic variety obtained by taking...
study of polynomials. The modulargroup may be realised as a quotient of the special linear group SL(2, Z). If n ≥ 2, then the group GL(n, F) is not abelian...
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...
setting in which congruence subgroups can be studied is that of the modulargroup S L 2 ( Z ) {\displaystyle \mathrm {SL} _{2}(\mathbb {Z} )} . If n ⩾...
group only being the orientation-preserving transformations. PGL and PSL can also be defined over a ring, with an important example being the modular...
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 modulargroup 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...
are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modulargroup, Eisenstein series...
The Volkswagen Group MEB platform (German: Modularer E-Antriebs Baukasten, 'modular electric-drive toolkit') is a modular car platform for electric cars...
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...
\backslash \mathbb {H} ^{2}} , where Γ {\displaystyle \Gamma } is the modulargroup, the Selberg zeta-function is of special interest. For this special...
name comes from the classical name modulargroup of this group, as in modular form theory. In string theory, modular invariance is an additional requirement...
topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms...
plane to the whole space. The modulargroup PSL(2,Z) is thought of as a discrete subgroup of PSL(2,R). The modulargroup is a lattice in PSL(2,R), but...
to this group as the "modulargroup of order 16", as its lattice of subgroups is modular. In this article this group will be called the modular maximal-cyclic...
Small modular reactors (SMRs) are a class of small nuclear fission reactors, designed to be built in a factory, shipped to operational sites for installation...
{\displaystyle \mathbb {C} } . An important example of this type of group is the Picard modulargroup SU ( 2 , 1 ; Z [ i ] ) {\displaystyle \operatorname {SU}...
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