Sentence examples for conjecture implied from inspiring English sources

The conjecture implied that, in the particular case of three-dimensional manifolds modeled on the three-dimensional sphere, the Poincaré conjecture is true.

It has been shown that the Vertex Conjecture implies the Edge Conjecture.

The conjecture implies the Riemann hypothesis for all Dirichlet zeta functions.

This conjecture implies the essential simplicity hypothesis that almost all zeros of the zeta-function are simple.

Note also that this conjecture implies that (q_{t}(x|mathcal {S}_{t}) to pi (x)) almost everywhere.

The Singer-Wermer conjecture implies that any linear derivation on a commutative semisimple Banach algebra is identically zero [11].

It was shown by Fornæss and Stensønes that a positive answer to the following conjecture implies a positive answer to Conjecture 1.

The conjecture implies that the identity |ζχ(s)−1| = ∏ |1−x(p p−s| is valid when s lies on the horizontal half-line to the right of a zero in the critical strip.

The conjecture implies that if a cooperative Boolean network and an initial condition are randomly chosen (without any restrictions on the number of inputs per node), the probability that a steady state is reached after only one step approaches 1 as the dimension of the network increases without bound.

More precisely he showed that the abc conjecture implies the existence of a constant only depending on α such that the number of non-Wieferich primes to base α with p less than or equal to a variable X is greater than log(X) as X goes to infinity.

From the considerations above, this conjecture implies that generic smooth four dimensional cubic is not rational, a standing question in algebraic geometry.