multiplicatively independent
A set of nonzero complex numbers is said to be multiplicatively independent iff every equation
with and implies that
For example, the set of prime numbers is multiplicatively independent, by the fundamental theorem of arithmetics
.
Any algebraically independent set is also multiplicatively independent.
Evidently, is multiplicativelyindependent if and only if the numbers , , …, are linearly independent over . Thus the Schanuel’s conjecture may be formulated as the
Conjecture. If is multiplicatively independent, then the transcendence degree of the set
is at least .
References
- 1 Diego Marques & Jonathan Sondow: Schanuel’s conjecture and algebraic powers and with and transcendental (2011). Available http://arxiv.org/pdf/1010.6216.pdfhere.