On the Lindemann-Weierstrass theorem (Q1382567)

The author proposes a new version of the proof of the classical Lindemann-Weierstrass theorem on the linear independence of the values of the exponential function at algebraic points. The Lindemann-Weierstrass theorem is implied by the following result. Let \(\alpha_0,\dots,\alpha_m\), \(a_0,\dots,a_m\) be algebraic numbers and the function \(A(t)\) be specified by the equality \[ A(t) = a_0e^{\alpha_0t} + a_1e^{\alpha_1t} + \dots + a_me^{\alpha_mt}, \] which is not identically zero. Then \(A(1) \neq 0\).