Stéphane Fischler

A new transcendence measure for the values of the exponential function at algebraic arguments

Let P ∈ ℤ [ X ] ∖ { 0 } be of degree δ ≥ 1 and usual height H ≥ 1 , and let α ∈ ℚ ¯ * be of degree d ≥ 2 . Mahler proved in 1931 the following transcendence measure for e α : for any ε > 0 , there exists c > 0 such that | P ( e α ) | > c / H μ ( d , δ ) + ε where the exponent μ (...