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Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

The set lambda of linear Möbius transformations w which satisfy w(t)=(at+b)/(ct+d), where a and d are odd and b and c are even. lambda is a subgroup of the modular group ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

If lim_(z->z_0)(f(z)-f(z_0))/(z-z_0) is the same for all paths in the complex plane, then f(z) is said to be monogenic at z_0. Monogenic therefore essentially means having a ...

sum_(k=0)^(infty)[((m)_k)/(k!)]^3 = 1+(m/1)^3+[(m(m+1))/(1·2)]^3+... (1) = (Gamma(1-3/2m))/([Gamma(1-1/2m)]^3)cos(1/2mpi), (2) where (m)_k is a Pochhammer symbol and Gamma(z) ...

A nonempty finite set of n×n integer matrices for which there exists some product of the matrices in the set which is equal to the zero matrix.

A Müntz space is a technically defined space M(Lambda)=span{x^(lambda_0),x^(lambda_1),...} which arises in the study of function approximations.

Let Omega be a space with measure mu>=0, and let Phi(P,Q) be a real function on the product space Omega×Omega. When (mu,nu) = intintPhi(P,Q)dmu(Q)dnu(P) (1) = ...

Two real algebraic manifolds are equivalent iff they are analytically homeomorphic (Nash 1952).

The natural parametric equations of a curve are parametric equations that represent the curve in terms of a coordinate-independent parameter, generally arc length s, instead ...