Four exponentials conjecture
From Wikipedia, the free encyclopedia
In mathematics, specifically transcendence theory, the four exponentials conjecture is a conjecture which, given the right conditions on the exponents, would guarantee the transcendence of at least one of four exponentials.
[edit] Statement
- If x1,x2 and y1,y2 are two pairs of complex numbers, with each pair being linearly independent over the rational numbers, then at least one of the following numbers is transcendental:
[edit] History
The related six exponentials theorem was first explicitly mentioned in the 1960s by Lang[1], and after proving the theorem he mentions the difficulty in dropping the number of exponents from six to four - the proof used for six exponentials “just misses” when one tries to apply it to four.
[edit] References
- ^ S. Lang, Introduction to transcendental numbers, Chapter 2 §1, Addison-Wesley Publishing Co., Reading, Mass., 1966.
