cuspidal , auch: cuspidate , auch: cuspidated

Ridge lines correspond to cuspidal edges on the focal surface.

A function occurring in such a space is called a cuspidal function.

For a hyperbolic umbilic there is a single cuspidal edge which switch from one sheet to the other.

What remains is the basic idea that representations in general are to be constructed by parabolic induction of cuspidal representations.

The unipotent cuspidal characters were listed by Lusztig using rather complicated arguments.

In geometry, a pinch point or cuspidal point is a type of singular point on an algebraic surface.

There is a large general theory, depending though on the quite intricate theory of parabolic subgroups, and corresponding cuspidal representations.

This includes Rankin-Selberg products for cuspidal automorphic representations of general linear groups.

In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in spaces.

The projection of C onto a plane from a point on a tangent line of C yields a cuspidal cubic.

Curves of types (ii) and (iii) are the rational cubics and are call nodal and cuspidal respectively.

When the group is the general linear group , the cuspidal representations are directly related to cusp forms and Maass forms.

For the case of cusp forms, each Hecke eigenform (newform) corresponds to a cuspidal representation.

The integral converges absolutely if one of the two forms is cuspidal; otherwise the asymptotics must be used to get a meromorphic continuation like Riemann did.

The Bernstein-Zelevinsky classification reduces the classification of irreducible smooth representations to cuspidal representations.

A cuspidal representation of G(A) is such a subrepresentation (π, V) for some ω.

Assuming conjectures 1 and 2 below, L-functions of irreducible cuspidal automorphic representations that satisfy the Ramanujan conjecture are primitive.

The Chisini conjecture in algebraic geometry is a uniqueness question for morphisms of generic smooth projective surfaces, branched on a cuspidal curve.

The Artin conjecture then follows immediately from the known fact that the L-functions of cuspidal automorphic representations are holomorphic.

A consequence for thinking about representation theory is that cuspidal representations are the fundamental class of objects, from which other representations may be constructed by procedures of induction.

The dual of a cuspidal character χ is (-1)χ, where Δ is the set of simple roots.

The unipotent characters can be found by decomposing the characters induced from the cuspidal ones, using results of Howlett and Lehrer.

Cuspidal automorphic representations of GL that are square integrable (modulo the center) at each ramified place of G.

These can be found from the cuspidal unipotent characters: those that cannot be obtained from decomposition of parabolically induced characters of smaller rank groups.

Thus for normalized cuspidal Hecke eigenforms of integer weight, their Fourier coefficients coincide with their Hecke eigenvalues.