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Modular form. In mathematics, a modular form is a (complex) analytic function on the upper half-plane, , that satisfies: a kind of functional equation with respect to the group action of the modular group, and a growth condition. The theory of modular forms therefore belongs to complex analysis. The main importance of the theory is its ...
e. In mathematics, the special linear group SL (n, R) of degree n over a commutative ring R is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant.
The braid group B 3 is the universal central extension of the modular group, with these sitting as lattices inside the (topological) universal covering group SL 2 (R) → PSL 2 (R). Further, the modular group has a trivial center, and thus the modular group is isomorphic to the quotient group of B 3 modulo its center ; equivalently, to the ...
Ring of modular forms. In mathematics, the ring of modular forms associated to a subgroup Γ of the special linear group SL (2, Z) is the graded ring generated by the modular forms of Γ. The study of rings of modular forms describes the algebraic structure of the space of modular forms.
Modular systems from the 60s and 70s, such as those produced by Moog, Buchla, Arp and Roland, had mainly become the domain of vintage instrument collectors, while the modular synthesisers that ...
The modular function is a continuous group homomorphism from G to the multiplicative group of positive real numbers. A group is called unimodular if the modular function is identically 1 {\displaystyle 1} , or, equivalently, if the Haar measure is both left and right invariant.
The CAMM ( Common Anti-Air Modular Missile) is a family of surface-to-air missiles developed by MBDA UK for the United Kingdom. CAMM is derived from, and shares some common features and components with, the Advanced Short-Range Air-to-Air Missile ( ASRAAM ), but with updated electronics, a soft vertical launch system, and an active radar homing ...
The Lie algebra of SL (2, R ), denoted sl (2, R ), is the algebra of all real, traceless 2 × 2 matrices. It is the Bianchi algebra of type VIII. The finite-dimensional representation theory of SL (2, R) is equivalent to the representation theory of SU (2), which is the compact real form of SL (2, C ).