 Writing "q" = "e"2π"i" for the nome and "j"() = "J"("q"), Daniel Bertrand conjectured that if "q"1 and "q"2 are non-zero algebraic numbers in the complex unit disc that are multiplicatively independent, then "J"("q"1) and "J"("q"2) are algebraically independent over the rational numbers.Although not obviously related to the four exponentials conjecture, Bertrand's conjecture in fact implies a special case known as the weak four exponentials conjecture.This conjecture states that if "x"1 and "x"2 are two positive real algebraic numbers, neither of them equal to 1, then π² and the product are linearly independent over the rational numbers.