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Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...

A

**conjecture**due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This**conjecture**implies the Bieberbach ...Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

The

**conjecture**that Frey's elliptic curve was not modular. The**conjecture**was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...A

**conjecture**that, as proved by Parshin (1968), implies the Mordell**conjecture**.The Cramér

**conjecture**is the unproven**conjecture**that lim sup_(n->infty)(p_(n+1)-p_n)/((lnp_n)^2)=1, where p_n is the nth prime.The kissing number of a sphere is 12. This led Fejes Tóth (1943) to

**conjecture**that in any unit sphere packing, the volume of any Voronoi cell around any sphere is at least ......