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A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

An expression that is of a given type. For example, all primes p>3 are "of the form" 6n+/-1. The term "of shape" is sometimes also used.

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the first fundamental form is the inner product of tangent vectors, ...

A function f is said to be an entire modular form of weight k if it satisfies 1. f is analytic in the upper half-plane H, 2. f((atau+b)/(ctau+d))=(ctau+d)^kf(tau) whenever [a ...

The kernel of a symmetric bilinear form Q:V×V-->R is the set Ker(Q)={v in V|Q(v,w)=0 for all w in V}.

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

For K a given knot in S^3, choose a Seifert surface M^2 in S^3 for K and a bicollar M^^×[-1,1] in S^3-K. If x in H_1(M^^) is represented by a 1-cycle in M^^, let x^+ denote ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...